Question

extra credit: use the given formula to generate the first for terms of each geometric sequence.
$g_n = 8240 \cdot 1.05^{n - 1}$
remember... $a_n = a_1 \cdot r^{n - 1}$
n = the term number
$a_1$ = the first term in the sequence
r = the common ratio

Explanation:

Step1: Calculate 1st term (n=1)

Substitute $n=1$ into $g_n = 8240 \cdot 1.05^{n-1}$:
$g_1 = 8240 \cdot 1.05^{1-1} = 8240 \cdot 1.05^0 = 8240 \cdot 1 = 8240$

Step2: Calculate 2nd term (n=2)

Substitute $n=2$ into the formula:
$g_2 = 8240 \cdot 1.05^{2-1} = 8240 \cdot 1.05^1 = 8240 \cdot 1.05 = 8652$

Step3: Calculate 3rd term (n=3)

Substitute $n=3$ into the formula:
$g_3 = 8240 \cdot 1.05^{3-1} = 8240 \cdot 1.05^2 = 8240 \cdot 1.1025 = 9084.6$

Step4: Calculate 4th term (n=4)

Substitute $n=4$ into the formula:
$g_4 = 8240 \cdot 1.05^{4-1} = 8240 \cdot 1.05^3 = 8240 \cdot 1.157625 = 9538.83$

Answer:

The first four terms are 8240, 8652, 9084.6, and 9538.83