Question

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

Answer 1

Sum of first 7 terms, S7 = 10 &
Sum of next 7 terms = 17
Sum of first 14 terms = 10+17 =27
Let First termm = a
Common difference = d
Sum of 'n' terms = (n/2){2a+(n-1)d}
Hence for first seven terms we have
10=(7/2){2a+(7-1)d} or 10 = 7a +21d
and for first 14 terms
27=(14/2){2a+(14-1)d} or 27 =14a +91d
Solving we get d=1/7 and a = 1
thus the ap is 1, 8/7, 9/7, 10/7....