Can anyone help with a math problem? Plz?

Question

if the first term of a finite geometric sequence is 0.9 and its ratio is 0.2, what is the sum of the first five terms?

Answer 1

We can find the answer to this question by using the formula for finding the sum of a finite G.P., which says that if the first term of a G.P. is 'a' & its common ratio is 'r', then the sum of 'n' terms of the G.P., S=a*(r^n - 1) / (r-1). So, lets use this formula in your question & get the answer.

In your question, first term, a=0.9
Common ratio, r=0.2
No of terms, n=5
Therefore, sum, S=a*(r^n - 1) / (r-1)
= 0.9 * (0.2^5 - 1) / (0.2 - 1)
= 0.9 * (-0.99968) / (-0.8)
= 0.9*1.2496
= 1.12464 (Answer)

Answer 2

The stunt to do these is to note that (1-i)(1+i+i^2+...+i^n) is 1-i^(n+1).