Question

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

Answer 1

Answer:

a(7) = -0.4

Step-by-step 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

Answer 2

Answer:

a₇ = - $\frac{2}{5}$

Step-by-step 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 = $\frac{a_{2} }{a_{1} }$ = $\frac{1250}{-6250}$ = - $\frac{1}{5}$ , then

a₇ = - 6250 × $(-\frac{1}{5}) ^{6}$ = - 6250 × $\frac{1}{15625}$ = $\frac{-6250}{15625}$ = - $\frac{2}{5}$