Question

the sum of certain number of terms of an AP is 155. find the number of term , given that the first term is 2 and the common difference is 3.

Answer 1

Sum of terms of A.P = 155
first term(a) = 2
common difference(d) = 3
S = n/2[2a+(n-1)d]
155 = n/2[2*2+(n-1)3]
155 = n/2[4+3n-3]
310 = n[1+3n]
310 = n+3n²
3n² + n - 310 = 0
3n² - 30n + 31n - 310 = 0
3n(n - 10) + 31(n-10) = 0
(n-10)(3n + 31) = 0
n = 10 or n = 31/3
31/3 is not possible so n=10
Number of terms = 10

Answer 2

S= n/2[2a+(n-1)d]
155=n/2[2×2+(n-1)3]
155×2=n[4+3n-3]
310=n[3n+1]
310=3n×n+n
3n×n+n-310= 0
3n×n+31n-30n-310=0
n(3n+31)-10(3n+31)=0
(3n+31) (n-10)=0
n=-31/3 or n=10