Question -
Answer -
Let Tn bethe nth term and Sn be the sum to n terms of the givenseries.
We have,
Sn = 3+ 7 + 14 + 24 + 37 + …………. + Tn-1 + Tn … (1)
Equation (1) can berewritten 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 betweenthe successive terms are 4, 7, 10, 13
So these differencesare in A.P
Now,
∴ The sum of the seriesis n/2 [n2 + n + 4]