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

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Solution

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

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