The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of

1.	The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
Answer» We have sum of n terms, S_n = 3n² + 4n Put n = 1 S₁ = T₁ = 3(1)² + 4 (1) = 7 Put n = 2 S₂ = 3(2)² + 4 (2) = 20 T₂ = S₂ – S₁= 20 – 7 = 13 Put n = 3 S₃ = 3(3)² + 4(3) = 39 T₃= S₃ – S₂ = 39 – 20 = 19 Therefore, first term is 7 and common difference, d = 13 – 7 = 6 The 25^th term is, T_n= a + (n – 1) d T₂₅ = 7 + (25 – 1) x 6 = 7 + 24 x 6 = 151

The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.

Answer»

We have sum of n terms,

S_n = 3n² + 4n

Put n = 1

S₁ = T₁ = 3(1)² + 4 (1) = 7

Put n = 2

S₂ = 3(2)² + 4 (2) = 20

T₂ = S₂ – S₁= 20 – 7 = 13

Put n = 3

S₃ = 3(3)² + 4(3) = 39

T₃= S₃ – S₂ = 39 – 20 = 19

Therefore, first term is 7 and common difference,

d = 13 – 7 = 6

The 25^th term is, T_n= a + (n – 1) d

T₂₅ = 7 + (25 – 1) x 6

= 7 + 24 x 6 = 151