What is the sum of the first 10 terms of the sequence defined by a_n = 3n - 3 ?

Solution:

The given nth term of the sequence is

a_n = 3n - 3

We have to determine the sum of the first 10 terms 

If n = 1

a₁ = 3(1) - 3 = 0

If n = 2

a₂ = 3(2) - 3 = 6 - 3 = 3

If n = 3

a₃ = 3(3) - 3 = 9 - 3 = 6

If n = 4

a₄ = 3(4) - 3 = 12 - 3 = 9

So the sequence is of the form 0, 3, 6, 9 ….

Here the first term a₁ = 0, d = 3 - 0 = 3

The formula to find the sum is

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

Substituting the values

S₁₀ = 10/2 [2(0) + (10 - 1) 3]

By further calculation

S₁₀ = 5 [0 + (9) 3]

S₁₀ = 5 [27]

S₁₀ = 135

Therefore, the sum of the first 10 terms is 135.

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What is the sum of the first 10 terms of the sequence defined by a_n = 3n - 3?

Summary:

The sum of the first 10 terms of the sequence defined by a_n = 3n - 3 is 135.