Question

In an A.P., the sum of its first n terms is 6n – n². Find is 25th term.

Answer 1

S_n = 6n – n²
T₂₅ = ?
S_(n–1) = 6(n – 1) – (n – 1)²
= 6n – 6 – (n² – 2n + 1)
= 6n – 6 – n² + 2n –1
= 8n – n² – 7
a_n = S_n – S_n – 1
= 6n – n² – 8n + n² + 7
= –2n + 7
a₂₅ = –2(25) + 7
= –50 + 7
= –43.