Question

The first term of a geometric sequence is 12 and the sum of the first two terms is 35.

Work out the sum of the first 10 terms of the sequence.

Give your answer as a decimal correct to 3 significant figures.

Answer 1

Answer:

8745.530

Step-by-step explanation:

a₁ = 12

S₂ = 12*(1-r²)/(1-r) = 35

12*(1+r)*(1-r)/(1-r) = 12(1+r) = 35

12r = 23           r = 23/12

S₁₀ = 12*(1-(23/12)¹⁰)/(1-(23/12)

     = 8745.530

Answer 2

The sum of the first 10 terms of the sequence will be 8745.530.

What is a geometric sequence?

A geometric sequence is a sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

Given that the first term of a geometric sequence is 12 and the sum of the first two terms is 35.

The sum of the first 10 terms will be calculated as below:-

a₁ = 12

S₂ = 12 x (1-r²)/(1-r) = 35

S₂ 12 x (1+r) x (1-r)/(1-r) = 12(1+r) = 35

12r = 23          

r = 23/12

The sum will be calculated as below:-

S₁₀ = 12x (1-(23/12)¹⁰)/(1-(23/12)

S₁₀ = 8745.530

Therefore, the sum of the first 10 terms of the sequence will be 8745.530.

Learn more about the geometric sequence here;

brainly.com/question/1509142

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