Assuming the first term as a and common difference as d

To find: the progression

So, the sum of first 7 terms is given by

a + a + d + a + 2d + a + 3d…. a + 6d = 10

7a + 21d = 10…(i)

In the second part it is given that sum of next seven terms is 17

a + 7d + a + 8d + a + 9d…. a + 13d = 7

7a + 70d = 7…(ii)

Solving (i) and (ii) we get

10 - 21d = 7 - 70d

3 = - 49d

Hence the sequence is given by a, a + d, a + 2d…. which is