Question

the sum of first four term of AP is 56 the sum of last four term is 112 if its first term is 11 then find the number of term

Answer 1

Sum of first four terms = 56
Sum = n/2*(A1 + An)
n=4, A1=11
56 = 4/2 *(11 + An)
28= 11 + An
An = 17 = A4
d = 2...[An = A1 +(n-1)*d...17 = 11 +3d..6 = 3d..d=2]

Now, given sum of last 4 terms = 112
n-3,n-2,n-1,n terms sum = 112
Applying A.P sum formula
112 = 4/2*(A(n-3) + An)
56 = (A1 + (n-3-1)d + A1 + (n-1)d).... [An-3 = A1 +(n-3 - 1)*d]
56 = (11 + (n-4)*2 + 11 + (n-1)*2)
56 - 22 = (n-4)*2 + (n-1)*2
34 = 2*(n-4+n-1)
17 = 2n-5
22 = 2n
n = 11
Hence number of terms = 11
Hope it helps.