Question

Find 40th term of a sequence if the sum of n terms is given by S_n = 3n² + 4n
1. 245
2. 241
3. 231
4. 251

Answer 1

Correct Answer - Option 2 : 241

Concept:

Sn is denoted sum of the n^th term 

We define S₁ = First term = a₁

S₂ = Sum of first 2 term = a₁ + a₂

S₃ = Sum of first 3 term = a₁ + a₂ + a₃

S_n = Sun of n^th term = a₁ + a₂ + a₃ + ........... + a_n

T_n is denoted number of terms

T_n = a + (n - 1)d

Here a = First term, d = Common difference(a₂ - a₁ = a₃ - a₂ = a₄ - a₃) and n = Number of term

Calculation:

Given: Sn = 3n2 + 4n

S₁ = 3(1)² + 4(1) = 7 = a₁

S₂ = 3(2)² + 4(2) = 12 + 8 = 20 = a₁ + a₂

a₁ + a₂ = 20

a₂ = 20 - 7 = 13

Common difference(d) = a₂ - a₁ = 13 - 7 = 6

First term a₁ = 7

T₄₀ is denoted 40^th term of the A.P.

T₄₀ = 7 + (40 - 1)6

T₄₀ = 7 + (39)6

T₄₀ = 7 + 234 = 241