Question

Find the 14th term of the geometric sequence 5 , − 10 , 20 ,

Answer 1

-40960

Explanation:

The formula for geometrc sequence is:

`\displaystyle{a_n = a_1r^(n-1)}`

Where r represents common ratio. In this sequence, our common ratio is -2 as -10/5 = -2 as well as 20/-10 = -2.

`a_1` represents the first term which is 5. Therefore, by substitution, we have:

`\displaystyle{a_n = 5(-2)^(n-1)}`

Since we want to find the 14th term, substitute n = 14. Thus:

`\displaystyle{a_(14) = 5(-2)^(14-1)}\\\\\displaystyle{a_(14)=5(-2)^(13)}\\\\\displaystyle{a_(14) = 5(-8192)}\\\\\displaystyle{a_(14)=-40960}`

Therefore, the 14th term is -40960.