For the following exercises, find the specified term for the geometric sequence, given the first four terms. an = {−1, 2, −4, 8, ...}. Find a12.

For the following exercises, find the specified term for the geometric sequence, given the first four terms.

an = {−1, 2, −4, 8, ...}. Find a12.

Expert Solution

Consider the following geometric sequence:

{=1, 2, -4, 8} ...... (1)

The first term of above sequence is a1 = -1.

Common ratio of the above sequence will be obtained by dividing its second term by the first term,

r = a2 ÷ a1

= 2 ÷ (-1)

= -2

Use the formula for nth term of a geometric sequence,

an = a1 × r(n-1) ...... (2)

Substitute a1 = 1, n = 12 and r = -2 in formula (1) and compute 12th term of the sequence,

a12 = (-1) × (-2)(12-1)

= (-1) × (-2)11

= (-1) × (-2048)

= 2048

Therefore, 12th term of the above geometric sequence is a12 = 2048.

Junaid answered 1 year ago

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Question

For the following exercises, find the specified term for the geometric sequence, given the first four terms. an = {−1, 2, −4, 8, ...}. Find a12.

Solutions

Expert Solution

Related Solutions

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