What is the sum of the first twenty terms of the arithmetic series 2 + 5 + 8 + 11 + 14 +… ?

Answer 1

Given sequence is 2, 5, 8, 11, 14, 17……,

The given sequence is in arithmetic progression as it has the same common difference which is 3,

So, now the sum of n terms in an arithmetic series can be written as,

S_n = n/2 [2a+(n−1)d],

Here we have to find the sum of 20 terms, so here n = 20,a = 2, d = 3, by substituting the value in the formulas we get,

 ⇒S₂₀ = 202[2(2)+(20−1)3],

Now simplifying we get,

⇒S₂₀ = 10[4+(19)3],

Now multiplying the terms inside the brackets we get,

⇒S₂₀ = 10[4+57],

Now again simplifying we get,

⇒S₂₀ = 10[61],

Now multiplying to simplify we get,

⇒S₂₀ = 610,

So, the sum of 20 terms is 610,

Now we have to find the 20th term of the given sequence, we know The nth term In A.P is given by T_n=a+(n−1)d,

By substituting the values in the formula we get, here n = 20,a = 2, d = 3, we get,

⇒T₂₀ = 2+(20−1)(3),

Now simplifying we get,

⇒T₂₀ = 2+(19)(3),

Now multiplying we get,

⇒T₂₀ = 2+57,

Now further simplification we get,

⇒T₂₀ = 59,

So, the 20th term is 59.

∴ The 20th term of the given sequence 2, 5, 8, 11, 14, 17…… is 59, and the sum of 20 terms of the sequence 2, 5, 8, 11, 14, 17…… is 610.