Question

How many term of the AP 6,10,14... are added to get 720

Answer 1

A1 = 6..... d=4
Sum = 720
Sum = n/2 * (A1 + An)
An = A1 + (n-1)d
Sum = n/2 * (A1 + A1 + (n-1)d)
720 = n/2 * (6 + 6 + (n-1)*4)
720*2 = n*(12 +(n-1)*4)
720*2 = 4*n*(3 + n - 1)
720*2/4 = n*(2+n)
360 = n*(n+2)
36*10 = n*(n+2)
18*2*10 = n*(n+2)
18*20 = n*(n+2)
Comparing above LHS & RHS part: n = 18, n+2 = 20
Hence, number of terms to get the sum = 720 is '18'
Hope it helps.