Question

Find a1, for the given geometric series. Round to the nearest hundredth if necessary. Sn= 86,830, r= 2.2, n=4

Answer 1

Answer:

4,646.30

Step-by-step explanation:

The sum of n terms of geometric sequence can be calculated using formula

$S_n=\dfrac{a_1(1-r^n)}{1-r}$

In your case,

$S_n=86,830\\ \\r=2.2\\ \\n=4\\ \\a_1=?$

Substitute into the formula:

$S_4=\dfrac{a_1(1-2.2^4)}{1-2.2}\\ \\86,830=\dfrac{a_1(1-23.4256)}{-1.2}\\ \\-104,196=a_1(-22.4256)\\ \\22.4256a_1=104,196\\ \\a_1=\dfrac{104,196}{22.4256}\approx 4,646.30$