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

daniko883y

daniko883y

Answered question

2022-10-08

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

Answer & Explanation

Domenigmh

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 = a n a n - 1
For example, if we take the ratio of the 2nd-to-1st terms, we get:
r = a 2 a 1 = -14 2 = -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 = ( -7 ) ( -686 ) = 4802

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