Question

The 5th term and 15th term of an AP are 13and 1/2 17 respectively find the sum of first 21st term of the AP

Answer 1

Let the first term be a, and d be the common difference  of an AP.So nth term tn =a + (n-1)d5th term =a+(5-1)d =13 a + 4d =13(i)15th term= a+(15-1)d=-17a+14d=-17 (ii)Solving (i) and (ii), we get a =25, d=-3Sum of n term =n2(2a+(n-1)d)So sum of 21 term=212(2×25+(21-1)×-3)= 212(50-60)=-105So the sum upto 21 terms =-105 Answer