3 + 7 + 14 + 24 + 37 + …
Solution:
Let Tn be the nth term and Sn be the sum to n terms of the given series.
We have,
Sn = 3 + 7 + 14 + 24 + 37 + …………. + Tn-1 + Tn … (1)
Equation (1) can be rewritten as:
Sn = 3 + 7 + 14 + 24 + 37 + …………. + Tn-1 + Tn ……..(2)
By subtracting (2) from (1) we get
Sn = 3 + 7 + 14 + 24 + 37 + …………. + Tn-1 + Tn
Sn = 3 + 7 + 14 + 24 + 37 + …………. + Tn-1 + Tn
0 = 3 + [4 + 7 + 10 + 13 + … + (Tn – Tn-1)] – Tn
The difference between the successive terms are 4, 7, 10, 13
So these differences are in A.P
Now,
∴ The sum of the series is n/2 [n2 + n + 4]