daniko883y

2022-10-08

Find the 5th term in the following geometric sequence 2, -14, 98, -686

Domenigmh

Beginner2022-10-09Added 7 answers

In a geometric sequence, each new term is the product of the previous term and a fixed multiplier r. (This is in contrast to an arithmetic sequence, where each new term is the sum of the previous term and a fixed additive value a.)

To find the multiplier r of a geometric sequence, simply take the ratio of any two consecutive terms already in the sequence.

$r=\frac{{a}_{n}}{{a}_{n-1}}$

For example, if we take the ratio of the 2nd-to-1st terms, we get:

$r=\frac{{a}_{2}}{{a}_{1}}=\frac{\text{-14}}{2}=\text{-7}$

Then, since we know the 4th term is -686, all we need to do is multiply this by our ratio r to get the 5th term:

${a}_{5}=r{a}_{4}=\left(\text{-7}\right)\left(\text{-686}\right)=4802$

To find the multiplier r of a geometric sequence, simply take the ratio of any two consecutive terms already in the sequence.

$r=\frac{{a}_{n}}{{a}_{n-1}}$

For example, if we take the ratio of the 2nd-to-1st terms, we get:

$r=\frac{{a}_{2}}{{a}_{1}}=\frac{\text{-14}}{2}=\text{-7}$

Then, since we know the 4th term is -686, all we need to do is multiply this by our ratio r to get the 5th term:

${a}_{5}=r{a}_{4}=\left(\text{-7}\right)\left(\text{-686}\right)=4802$

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