Question

find the sum of first 25 terms of an ap whose nth term is 1- 4n

Answer 1

Here it is given that, an = 1 - 4n

putting, n =1 , a1 = 1- 4(1) = -3

putting, n =2 , a2 = 1 - 4(2) = -7

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

so, S25 = 25/2 [ 2(-3) + 24 (-4)]

= 25/2 [-102]

= 25 (-51 )

= -1275 Ans

hence, the sum of first 25 terms of an AP whose nth term is 1 -4n is -1275.

Answer 2

given
tn=1-4n
but we know tn=a+(n-1) d
=(a-d)+nd
compare both equation
1=a-d
d=-4
so, a =1+d=-3
now sum of 25 terms =25/2 {2 x (-3)+(25-1)(-4)} =25(-3-48)=25 x (-51)
=-1275