Question

A geometric sequence starts at 10 and each successive term is 1.1times the previous term. Thus a1=10 and f=1.1.

What is the sum of the first 100 terms?
A) 1.378 million

B )3.378 million

C) 3.877 million

D) 1.783million

Answer 1

To find the sum of the first 100 terms of a geometric sequence, we can use the formula:

S = a(1 - f^n) / (1 - f)

where S is the sum of the first n terms, a is the first term, f is the common ratio, and n is the number of terms.

In this case, a = 10, f = 1.1, and n = 100. So we have:

S = 10(1 - 1.1^100) / (1 - 1.1)

S = 10(1 - 2.98551 x 10^7) / (-0.1)

S = 10(-2.98551 x 10^7 + 1) / 0.1

S = -2.98551 x 10^8 + 10

S = 3.7949 x 10^6

Therefore, the sum of the first 100 terms is approximately 3.7949 million. The closest answer choice to this value is C) 3.877 million, but none of the answer choices match the calculated value exactly.