Question

find the sum of how many terms of the AP 10 12 14.....
will be 1 90

Answer 1

Sn = 190
a= 10
d = a1-a2 = 12 - 10 = 2

Sn = n/2 ( 2a + (n-l)d)
190 = n/2 (2*10 + (n-1)2)
190*2 = n (20 +2n -2)
380 = n (18 + 2n)
380 = 18n + 2n^2



By using mid term splitting formula
2n^2 + 18n - 380 =0
2n^2 + 38n - 20 n -380 =0
2n ( n + 19 ) - 20 ( n + 19 ) =0
(2n-20) (n+19) =0
n= 10 or n=-19 =0
hence , n can't be -19 so no. of the term is 10.