the nth term of a geometrc sequence is given by an=27(0.1)^n-1

a. write the first 5 terms of sequencwe

b.use formula for sum of geometric series to find the sum of first 10 terms of sequence.

PLS B THOROUGH AND SHOW ALL StEPS

Hi there! Thank you for the opportunity to help you with your question!

The first n terms are found by replacing n= 1, n =2, n =3, n =4 and n=5, wherever you see "n" in the expression an=27(0.1)^(n-1)

Therefore:

a1 = 27*(0.1)^(1-1) = 27*(0.1)^0 = 27*1 = 27

a2 = 27*(0.1)^1 = 27*0.1 = 2.7

a3 = 27*(0.1)^2 = 27*.01 = 0.27

a4 = 27*(0.1)^3 = 27*.001 = 0.027

a5 = 27*(0.1)^4 = 27*0.0001 = 0.0027

In summary, this is a geometric series, with initial term 27 and ratio between terms = 0.1 we have the formula:

sum(an) from 1 to 10 = 27*sum(0.1^(n-1)) from 1 to 10

The formula is given by 27* (1- 0.1^9)/(1-0.1) = 30

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