Question

D. 6

In a geometric series, the sum of the first 4 terms is 80 and the common ratio is 3, what is the first term?
C. 4
B. 3
A. 2
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Answer 1

Hi,

answer A:2

Explanation:

In a geometric series, the sum of the first 4 terms can be calculated using the formula:

`S_n=(a(1-r^n))/(1-r) \\`

where:

Sn​ is the sum of the first nn terms,

a is the first term of the series,

r is the common ratio, and

n is the number of terms.

In this case, you are given that the sum of the first 4 terms (S4​) is 80, and the common ratio (r) is 3. You want to find the first term (a).

So, you have:

S4=80

r=3

You can rearrange the formula to solve for aa:

`a=S4*(1-r)/(1-r^4) \\`

Plugging in the values and simplify the egality:

a=80(1−3)/(1−3^4)=80*(-2)/(−80)​=2.

So, the first term of the geometric series is a=2.

So, the correct answer is A. 2.