The sum of first 7 terms of an AP is 10 and that of next 7 terms is 17.

Solution:

To Find: AP

Given: Sum of first 7 terms $=10$

Sum of next 7 terms $=17$

According to the problem,

Sum of first 14 terms of the given AP is $10+17=27$.

So we can say $10=\frac{7}{2}(2 a+6 d)$ and $27=\frac{14}{2}(2 a+13 d)$

Solving the equations we get $14 a+42 d=20 \ldots$ (i) and

$14 a+91 d=27 \ldots(i i)$

Subtracting (i) from (ii)we get 49d = 7

$\Rightarrow d=\frac{1}{7}$

Therefore from $(i), 14 a=20-42 \times \frac{1}{7}$

$\Rightarrow a=1$

The series is $1,1 \frac{1}{7}, 1 \frac{2}{7}, 1 \frac{3}{7} \ldots$