Question

Find the sum of following series upto terms 1+9+24+46+...

Answer 1

Given s = 1 + 9 + 24 + 16 -----  n.

Following are the steps to solve this : 

1.  0 + 1 + 9 + 24 + 46 + --- n

As u can the common difference is 7 i.e 1 + 8 + 15 + 22.

2. The formula for quadratic sequence when the second difference is 7, you should start with 3n^2 i.e

  = 3.5 n^2 - 2n

3. Sum of squares formula is n(n+1)(2n+1)/6 i.e

   = 3.5/6 n(n+1)(2n+1)                 ----------------------- (i) 

4. Sum of integers is n(n+1)/2

  = -2.5/2 n(n+1)                          ----------------------  (ii)


On solving (i) and (ii) we get:

S(n) = (1/6)(n)(7n^2+3n-4)


Hope this helps!