(Q30).Show that a1, a2 …,an, …. form an AP where an is defined as below:

(ii) an = 9 – 5n

Given an = 9 – 5n.

Then a1 = 9 – 5 × = 9 – =

a2 = 9 – 5 × = 9 – = -

a3 = 9 – 5 × = 9 – = -

a4 = 9 – 5 × = 9 – = -

Also

a2 – a1 = - – = -;

a2 – a1 = - – (-) = – 6 + = -

a3 – a2 = - – (-) = - + = -

∴ d = a2 – a1 = a3 – a2 = a4 – a3 = …. = -

Thus the difference between any two successive terms is constant (or) starting from the second term, each term is obtained by adding a fixed number ‘-’ to its preceding term.

Hence {an} forms an A.P.

S15 =
2
 [2 × + (-1) × (-)]
=
2
 [ + (-)] =
2
 × -

= × - = -