Question

Determine whether the sequence converges or diverges. If it converges, give the limit. 11, 44, 176, 704, ...

Answer 1

Hey Mate!!

1) Note that we multiply by 4 to get from term to term.

So we have the geometric sequence a(n) = 11 * 4^(n-1) for all n = 1, 2, 3, ...

Since |r| = 4 > 1, this sequence diverges.

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2) Note that a(n) = a(1) + (n - 1)d, where d is the common difference between consecutive terms.

In this case, d = a(16) - a(15) = -5 - (-53) = 48.

So, a(n) = a(1) + 48(n - 1).

To find a(1), I will use a(15) = -53.

Letting n = 15, we obtain -53 = a(1) + 48 * (15 - 1).

==> a(1) = -725.

So, we have a(n) = -725 + 48(n - 1) = 48n - 773.

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3) We multiply -6 to get from term to term. (Hence, this series is geometric.)

So, this equals Σ(n = 1 to ∞) 2 * (-6)^(n-1).

Answer 2

Answer:

The term to term rule is multiplying by 4 and if we continue doing this, we will move towards very large positive numbers.This sequence, therefore, diverges to infinity.