Question

Find the indicated terms in each of following A.P.s: – 4, – 7, – 10, – 13, …, a₂₅, a_n

Answer 1

– 4, – 7, – 10, – 13, …, a₂₅, a_n 
Here, a = – 4, d = – 7 –  (– 4)
= – 7 + 4
= – 3
a₂₅ = a + (n – 1)d
= –4 + (25 – 1) x –3
= –4 + 24 x (–3)
= –4 – 72
= –76
and
an = a_n + (n – 1)d
= –4 + (n – 1) (–3)
= –4 – 3n + 3
= –1 – 3n
= –3n – 1.