Question

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Answer 1

This is my answer. Check it!

Answered by Benjemin

Answer 2

Answer:

• See below

Step-by-step explanation:

Let us have:

• a - the first term
• r - common ratio
• l - the last term

Formula of nth or last term:

• l = arⁿ⁻¹

The sequence:

• a, ar, ar², ..., arⁿ⁻¹

The sum of the sequence is:

• S = a + ar + ar² + ... + arⁿ⁻¹

Lets multiply the sum by r and subtract the sum:

• rS = ar + ar² + ar³ + ... + arⁿ
• S = a + ar + ar² + ... + arⁿ⁻¹
• rS - S = arⁿ - a = r(arⁿ⁻¹) - a = lr - a

Solve this for S:

• S(r - 1) = lr - a
• S = (lr - a)/(r - 1)

So we have a sum formula determined by the first, last terms and the common ratio.