# The sum of the first 7 terms of an A.P. is 10, and that of the next 7 terms is 17. Find the progression.

Given: Sum of first 7 terms, S7 = 10

and Sum of the next 7 terms = 17

Sum of 8th to 14th terms = 17

Sum of first 14 terms – Sum of first 7 terms = 17

S14 – S7 = 17

S14 – 10 = 17

S14 = 27

Sum of 7 terms,

20 = 7[2a + 6d]

20 = 14a + 42d …(i)

Sum of 14 terms,

27 = 7[2a + 13d]

27 = 14a + 91d …(ii)

Solving the linear equations (i) and (ii), we get

14a + 42d – 14a – 91d = 20 – 27

-49d = -7

Putting the value of d in eq. (i), we get

20 = 14a + 42d

20= 14a + 6

20 – 6 = 14a

14 = 14a

a = 1

Thus, a = 1 and

So, AP is

a1 = 1

a2

a3

Hence, AP is

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