Question

Find a1 if Sn = 89,800, r = 3.4, and n = 10. Round to the nearest hundredth if necessary.

Answer 1

Answer:

$a_1=1.04$

Step-by-step explanation:

We have a geometric  sequence with:

$Sn = 89,800$, $r = 3.4$, and $n = 10$

Where

Sn is the sum of the sequence

r is the common ratio

$a_1$ is the first term in the sequence

n is the number of terms in the sequence

The formula to calculate the sum of a finite geometric sequence is:

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

Then:

$89,800=\frac{a_1(1-(3.4)^{10})}{1-3.4}$

Now we solve for $a_1$

$89,800(1-3.4)=a_1(1-(3.4)^{10})$

$a_1=\frac{89,800(1-3.4)}{1-(3.4)^{10}}\\\\a_1=1.04$