Question

Find the sum of first 25terms of an A. P. whose nth term is given by an =2-3n

Answer 1

An = 2 - 3n

=> a +(n-1)d = - 1 + 3 - 3n

=> a +(n-1)d = - 1 - 3(n-1)

On comparing both sides, we get

a = - 1

d = - 3

S25 = 25/2 [ 2(-1) +(25-1)(-3)]

S25 = 25/2 [ - 2 - 72]

S25 = 25 × ( - 74) / 2

S25 = 25 × (-37)

S25 = - 925

Answer 2

Given that, Tn=2 -3n

Putting the value of n =1,then
T1 = 2-3*1
=-1

Putting the value of n=2 ,then
T2 =2 -3*2
=2-6
=-4

Therefore, a= -1 and d= -4-(-1) =-4+1=-3

Sn= n/2 {2a +(n-1)d}

S25 =25/2 {2*-1+(25-1)-3}

= 25/2 {-2-72}

= 25/2 *-74

= 25 * -37

= -925