Question

7. The sum to n term of an AP is 18. The common difference Is 3 and the sum to 3n terms is 135 . find the sum of the first 20 terms of the progression.​​​

Answer 1

The sum of the first 20 terms of the progression is 120

How to find the sum of the first 20 terms of the progression?

The given parameters are:

• Common difference, d = 3
• Sum to n terms = 18
• Sum to 3n terms = 135

The sum of the first n terms of an arithmetic progression is

Sn = n/2[2a + (n - 1) * d]

So, we have:

S3n = 3n/2[2a + (3n - 1) * d]

Substitute Sn = 18 and S3n = 135 and d = 3

So, we have:

n/2[2a + (n - 1) * 3] = 18

3n/2[2a + (3n - 1) * 3] = 135

Simplify each equation

n[2a + (n - 1) * 3] = 36

n[2a + (3n - 1) * 3] = 90

Expand

[2an + 3n(n - 1)] = 36

[2an + 3n(3n - 1)] = 90

Using a graphing calculator, we have:

a = 3 and n = 3

The sum of the first 20 terms is:

Sn = n/2[2a + (n - 1) * d]

This gives

S20 = 20/2 * [2 * 3 + (3 - 1) * 3]

Evaluate

S20 = 120

Hence, the sum of the first 20 terms of the progression is 120

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