Sequence & Series III(Lowersixth Science Mathematics)

Froggy Jumps

Parties jouées 0

Créer une copie

À propos de cette activité

Challenge on GP sums and sigma basics.

Créé par

YAKILI LMS

Cameroon

Téléchargez la version pour jouer sur papier

Créez votre propre jeu gratuite à partir de notre créateur de jeu

Affrontez vos amis pour voir qui obtient le meilleur score dans ce jeu

Créer un défi

Phlebotomy Order of Draw Quiz

Pamela Chapman

United States

(61)

Test your knowledge of the order of draw in Phlebotomy with these 10 questions!
Bill of Rights Game - The Constitutionalist

Doni The Don

United States

(92)

Test your knowledge on the Bill of Rights. A fun way to test your knowledge and focus on where you need to improve.
The Integumentary System

Breanna Nesbitt

United States

(59)

Functions and Structures of the skin
pizza

Lorelay Tyana

Romania

(266)

joc despre pizza
Ethos, Pathos, and Logos Quiz

Kristine Vester

United States

(134)

Test your knowledge of ethos, pathos, and logos with these 10 questions on examples of persuasive techniques.

		%
	Anonyme	%
		%
		%

Imprimez votre jeu

Sequence & Series III(Lowersixth Science Mathematics)


Froggy Jumps Sequence & Series III(Lowersixth Science Mathematics)Version en ligne Challenge on GP sums and sigma basics. par YAKILI LMS 1 What is the sum of the first n terms of a GP with first term a and ratio r (r ≠ 1)? a a(r^n−1)/(r−1) b a(1+r^n)/(1+r) c a(1−r^n)/(1−r) 2 What is the condition for convergence of the sum to infinity of a GP? a \|r\| > 1 b r ≠ 0 c \|r\| < 1 3 AM and GM relate by which inequality for positive numbers? a AM ≥ GM b AM ≤ GM c GM > AM 4 What principle is used to prove statements for all n in mathematics? a Mathematical induction b Contradiction c Direct proof 5 Sigma notation is used to denote what? a Product b Difference c Summation 6 Which symbol denotes a summation from i = 1 to n? a ∑i=1^n b Π from i=1 to n c Σ from i=1 to n 7 Sum to infinity of a GP with a and r equals what? a a/(1+r) b ar/(1−r) c a/(1−r) 8 What is the sum of a GP when r = −1/2 and a = 6 for n terms? a 6(1−(−1/2)^n)/(1+1/2) b 6(1−(−1/2)^n)/(1−1/2) c 6(1+(−1/2)^n)/(1+1/2) 9 If a = 3 and r = 2, sum of first n terms is? a 3(2^n−1)/(2−1) b 3(2^n−1)/1 c 3(1−2^n)/(1−2) 10 What is the general term of a GP? a a_n = a + nr b a_n = a/n * r c a_n = ar^(n−1) 11 What does Σi=1^n i represent? a Sum of integers from 1 to n b Sum of even numbers c Product of 1 to n 12 Which is a property of sigma notation? a Non-associative b No distributive rule c Linearity: Σ(a+b)=Σa+Σb 13 Which is true for AM-GM equality case? a All different b All numbers equal c Sum is zero 14 Sum to infinity exists only if r is? a \|r\| > 1 b r = 0 only c \|r\| < 1 15 What is the sum of the first n natural numbers? a n(n+1)/2 b n(n−1)/2 c n^2/2 16 Which series can be summed with induction proof? a Only finite series b Most arithmetic sequences c Only geometric series 17 What is the formula for sum of GP with a and r when r ≠ 1? a a(1+r^n)/(1+r) b a(1−r^n)/(1−r) c a(r^n−1)/(r−1) 18 What does Sigma notation with lower index mean? a Start term index b Difference index c End term 19 If a GP has r = 1, what is the sum of n terms? a a/n b an c a + nr 20 What is the sum of a GP with a=5, r=0.5, n=3? a 5(1−0.5^3)/1.5 b 5(1−0.5^3)/0.5 c 5(1−0.5^3)/1 21 Which is a correct sigma property? a Σ(a_i×c)=Σa_i×c^2 b Σ(ca_i)=cΣa_i c Σ(a_i+c)=Σa_i+c 22 AM-GM applies to which numbers? a Negative numbers only b Non-negative numbers c Always positive 23 What is an arithmetic mean of 4 and 10? a 6 b 8 c 7 24 What is the geometric mean of 4 and 9? a 6 b 3 c 12 25 What is the sum of first n terms of GP when r ≠ 1? a a(1−r^n)/(1−r) b a(1+r^n)/(1+r) c a(r^n−1)/(1−r) 26 Which involves induction base case? a Assuming P(n) is true b Proving P(1) is true c Proving P(n+1) is true without P(n) 27 Which is a convergent GP requirement? a \|r\|<1 b r≤0 and \|r\|≥1 c r>1 28 What is the sum to infinity for a GP with a=8 and r=1/3? a 8/(1−1/3)=24 b 8/(1+1/3)=6 c 8/(1−1/3)=12 29 Which notation means sum over k from 1 to n? a Π_{k=1}^n b ∫_{1}^{n} c Σ_{k=1}^n 30 What is the sum of integers 1 to 100? a 10000 b 5050 c 505 31 In sigma notation, what does the index i do? a Specifies terms summed over b Represents a coefficient c Indicates product 32 Which is not a GP property? a Terms increase by adding constant b Ratios constant c Each term multiplies by r 33 Sum of GP when a=2, r=−1/2, n=4 equals? a 2(1−(−1/2)^4)/(1+1/2) b 2(1−(−1/2)^4)/(1−(−1/2)) c 2(1+(−1/2)^4)/(1−(−1/2)) 34 Which identity is used in sigma linearity? a Σ(a−b)=Σa−Σb^2 b Σ(a×b)=Σa×Σb c Σ(a+b)=Σa+Σb 35 Which sequence has an constant ratio? a Harmonic sequence b Geometric sequence c Arithmetic sequence 36 If S_n is sum of GP terms, S_n is function of? a a, r, n b Only n c Only a 37 What is the AM of numbers 2, 8, 18? a 6 b 8 c 9 38 Induction proof typically has base case and? a Hypothesis only b Inductive step c Counterexample 39 Sum of first n terms of AP is? a n/2(a+nd) b n(a+nd)/2 c n/2[2a+(n−1)d] 40 What does Σi^n i^2 represent? a Sum of squares 1^2+...+n^2 b Sum of cubes c Product of squares 41 Which is a correct GP term formula? a a_n = ar^(n−1) b a_n = a/n c a_n = a + nr^2 42 What is the property Σ(a_i b_i) if a_i constant? a Cannot simplify b Always zero c b_i can be pulled out 43 What is the sum of negatives in a GP with r<0? a Always positive b Depends on n and r c Always negative 44 What is the sum of 1+1/2+1/4+... to n terms? (a=1, r=1/2) a 1(1−(1/2)^n)/(1−1/2) b (1−(1/2)^n)/(1+1/2) c n/2 45 Which is not a valid sigma notation form? a Σ_{i=1}^n i b Σ_i=1^n i c ∑_{i=1}^n i 46 Which describes convergence of infinite GP? a Limit of terms tends to 0 when \|r\|<1 b Sum always finite c Only if a=0 47 What is the base of induction? a P(1) true b P(n) false c P(n+1) assumed 48 Which is a correct AM-GM example? a (x−y)/2 ≤ √(xy) b For x,y>0, (x+y)/2 ≥ √(xy) c x+y ≤ 2√(xy) 49 What is the sum of 3 terms of GP: a=4, r=3? a 4(1−27)/(1−3) b 4(27−1)/(1−3) c 4(1−27)/(3−1) 50 What does the symbol Σ denote? a Multiplication b Differentiation c Summation

Sequence & Series III(Lowersixth Science Mathematics)

Froggy Jumps

À propos de cette activité

Créé par

Téléchargez la version pour jouer sur papier

Top Jeux

Froggy Jumps

Phlebotomy Order of Draw Quiz

Froggy Jumps

Bill of Rights Game - The Constitutionalist

Froggy Jumps

The Integumentary System

Froggy Jumps

pizza

Froggy Jumps

Ethos, Pathos, and Logos Quiz

Froggy Jumps

Sequence & Series III(Lowersixth Science Mathematics)Version en ligne

par YAKILI LMS

What is the sum of the first n terms of a GP with first term a and ratio r (r ≠ 1)?

What is the condition for convergence of the sum to infinity of a GP?

AM and GM relate by which inequality for positive numbers?

What principle is used to prove statements for all n in mathematics?

Sigma notation is used to denote what?

Which symbol denotes a summation from i = 1 to n?

Sum to infinity of a GP with a and r equals what?

What is the sum of a GP when r = −1/2 and a = 6 for n terms?

If a = 3 and r = 2, sum of first n terms is?

What is the general term of a GP?

What does Σi=1^n i represent?

Which is a property of sigma notation?

Which is true for AM-GM equality case?

Sum to infinity exists only if r is?

What is the sum of the first n natural numbers?

Which series can be summed with induction proof?

What is the formula for sum of GP with a and r when r ≠ 1?

What does Sigma notation with lower index mean?

If a GP has r = 1, what is the sum of n terms?

What is the sum of a GP with a=5, r=0.5, n=3?

Which is a correct sigma property?

AM-GM applies to which numbers?

What is an arithmetic mean of 4 and 10?

What is the geometric mean of 4 and 9?

What is the sum of first n terms of GP when r ≠ 1?

Which involves induction base case?

Which is a convergent GP requirement?

What is the sum to infinity for a GP with a=8 and r=1/3?

Which notation means sum over k from 1 to n?

What is the sum of integers 1 to 100?

In sigma notation, what does the index i do?

Which is not a GP property?

Sum of GP when a=2, r=−1/2, n=4 equals?

Which identity is used in sigma linearity?

Which sequence has an constant ratio?

If S_n is sum of GP terms, S_n is function of?

What is the AM of numbers 2, 8, 18?

Induction proof typically has base case and?

Sum of first n terms of AP is?

What does Σi^n i^2 represent?

Which is a correct GP term formula?

What is the property Σ(a_i b_i) if a_i constant?

What is the sum of negatives in a GP with r<0?

What is the sum of 1+1/2+1/4+... to n terms? (a=1, r=1/2)

Which is not a valid sigma notation form?

Which describes convergence of infinite GP?

What is the base of induction?

Which is a correct AM-GM example?

What is the sum of 3 terms of GP: a=4, r=3?

What does the symbol Σ denote?