14. Let a1, a2, a3, ... be the sequence defined by a₁ = 1, and for k ≥ 1, ak+1 k² ak. = Find the first six terms of this sequence. Guess a general formula for an and prove your answer by mathematical induction.

Q: Write an explicit formula for an, the nth term of the sequence 8, –4, 2, ....

A:

Q: Prove by induction that the sun of the first n terms of the sequence 17,20,23,26 is given by the…

A: The given sequence is .The sum of the first  terms of the sequence is .The aim is to prove the sum…

Q: Suppose that b₁ D₂ Dzi is a sequence defined as follows. bk = 5b ³|k/21] b₁ = 0 and b₂ = 3 True or…

A:

Q: 6 and an = 3an-1-4n, where n > 1 a₁ = O 6, 10, 18, 38, and 92 O 6, 12, 18, 38, and 94 O 6, 10, 18,…

A: We have to find the first five terms of the given sequence

Q: 1. Find he fifth term of the that has an nth term of (-1)! sequence - 730 D 120 (E)these noneof a…

A:

Q: 3. Use iteration to guess an explicit formula for the sequence. Simplify your answer if possible.…

A: Use iteration to guess an explicit formula for the sequence.

Q: Show for all integers n> 1 that 7 I (3ªn+l – 5²n-1 ).

A: a) Prove 734n+1-52n-1 for all integers n≥1 by mathematical induction as follows. Basis step: For…

Q: 5. Use polynomial fitting to find a closed formula for the sequence (ªn)n € N₁: 1,3, 11, 31, 69, ...

A:

Q: 4. Define the sequence an by a, = 1, a, = 33, and an = 3an-1+ 10an-2 for n 2 3. Prove that an = 5" –…

A: Concept used :- we use mathematical induction to solve the given question.

Q: 5. Suppose b₁,b2, b3, ... is a sequence defined as follows: b₁ = 4, b₂ = 12 bk = bk-1 + bk-2 for all…

A:

Q: Use the iteration method to write an explicit formula for the sequence that satisfies ao = 5 and ar…

A: The iteration method is the method in which the formula for a sequence can be obtained by…

Q: Suppose that g1, 92,93, ... is a sequence defined as follows: 91 = 3, 92 = 5, gk = 3gk-1 - 2gk-2 for…

A:

Q: 12. Suppose the sequence ao, aj, a2, a3, ... is defined as follows: ao = 0, aj = 1, and for n > 2,…

A:

Q: Let bo, b,, b2, ... be the sequence defined by the explicit formula b, = C. 6" + D(-5)^ for each…

A: Substitute 0 and 1 in the given expression to obtain the values of C and D,

Q: a. Write the first 10 terms of the Fibonacci sequence. 1 (1+ V5 2 calculator to verify this…

A: a) First term= 1 Second term= 1 Third term=1+1=2 Fourth term=2+1=3 Fifth term=2+3=5 Sixth term=3+5=8…

Q: Give an explicit formula for an, the apparent   nth term in the sequence 7, 17, 7, 17, 7, 17...

A: .

Q: Suppose that b1, b2, b3, . . is a sequence defined as = 12, b = br–1 + b-2 for each integer k > 3.…

A:

Q: 6. Let {an}1 be a sequence. If a1 = 1 and An+1 :2an + 1, use induction to prove an = 2" – 1. %3|

A: given that:-              an =1 and an+1 =2an+1  now, to prove  an=2n-1 we use induction.