Question

Find the 7th term of the geometric progression which begins -6250, 1250, -250....

Answer 1

a₇ = -
`(2)/(5)`

Explanation:

The nth term of a geometric progression is

`a_(n)` = a₁
`r^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = - 6250 and r =
`(a_(2) )/(a_(1) )` =
`(1250)/(-6250)` = -
`(1)/(5)` , then

a₇ = - 6250 ×
`(-(1)/(5)) ^(6)` = - 6250 ×
`(1)/(15625)` =
`(-6250)/(15625)` = -
`(2)/(5)`

Answer 2

a(7) = -0.4

Explanation:

The general formula for a geometric progression is a(n) = a(1)*r^(n - 1), where r is the common ratio. In this problem, a(1) = -6250. To find r, we divide 1250 (the 2nd term) by -6250 (the 1st term), obtaining r = -0.2.

Then the formula for THIS geometric progression is

a(n) = -6250*(-0.2)^(n - 1).

Thus, the 7th term of THIS progression is

a(7) = -6250*(-0.2)^(7 - 1), or -6250*(-0.2)^6, or -0.4