Answer:
The first term of the series is 4
Step-by-step explanation:
The sum of the first 6 terms of a geometric series is 15 , 624 and the common ratio is 5 .
To find the first term, we use the formula for the sum of terms in a geometric series.
Since the common ratio of the series is greater than 1, the sum of [tex]n^{th}[/tex] term of the geometric series is;
[tex]S = \frac{a(r^n - 1)}{r - 1}[/tex]
where r = common ratio
a = first term
When S = 15,624, r = 5 and n = 6, the first term, a, will be:
[tex]15624 = \frac{a(5^6 - 1)}{5 - 1} \\\\15624 = \frac{a(15625 - 1)}{4}\\\\15624 = \frac{a(15624)}{4}\\\\a = \frac{4 * 15624}{15624}[/tex]
a = 4
The first term of the series is 4.
