find the sum of the first 5 terms 4 12 36 108
Answer:
To find the sum of the first 5 terms of the geometric sequence 4, 12, 36, 108, we can use the formula for the sum of a geometric series:
S = a * (1 - r^n) / (1 - r)
Where:
S is the sum of the series,
a is the first term,
r is the common ratio,
and n is the number of terms.
In this case:
a = 4 (the first term)
r = 3 (the common ratio, as each term is obtained by multiplying the previous term by 3)
n = 5 (the number of terms)
Let's calculate the sum:
S = 4 * (1 - 3^5) / (1 - 3)
= 4 * (1 - 243) / (-2)
= 4 * (-242) / (-2)
= 484
Therefore, the sum of the first 5 terms of the geometric sequence 4, 12, 36, 108 is 484.