Question

The nth term of a geometric sequence is given by an=27 (0.1)^n-1 use the formula for the sum of a geometric series to find the sum of the first 10 terms of this sequence

Answer 1

the answer is 29.999

Explanation:

If you take the same equation used to find the first 5 terms you are able to find the sum of the first 10

Answer 2

29.999999997

Explanation:

Comparing the given formula to the general formula for the terms of a geometric sequence ...

an = a1·r^(n-1)

we see that ...

a1 = 27

r = 0.1

The formula for the sum of n terms of a geometric sequence is ...

Sn = a1·(1 -r^n)/(1 -r)

The sum of 10 terms of this sequence is ...

S10 = 27·(1 -0.1^10)/(1 -0.1) = 29.999999997

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Additional comment

Some calculators may have trouble with this. The correct answer has 11 significant digits. Some calculators only display 10 digits.