30. If the 1st term of a series is 7 and 13thterm is 35. Find the sum

1.	30. If the 1st term of a series is 7 and 13thterm is 35. Find the sum of 13 terms of[CBSE.2012]the sequence.
Answer» nth term of AP = a + (n-1)d 13th term = a + 12d Given a = 7 35 = 7 + 12d 12d = 28d = 28/12 = 7/3 Sum of n terms of AP = n/2(2a + (n-1)d) Sum of first 13 terms = 13/2(27 + 12(7/3))= 13/2(14 + 47)= 13/2(14 + 28)= 13/2(42)= 13*21= 273 ans

30. If the 1st term of a series is 7 and 13thterm is 35. Find the sum of 13 terms of[CBSE.2012]the sequence.

Answer»

nth term of AP = a + (n-1)d

13th term = a + 12d

Given a = 7

35 = 7 + 12d 12d = 28d = 28/12 = 7/3

Sum of n terms of AP = n/2(2a + (n-1)d)

Sum of first 13 terms = 13/2(2*7 + 12*(7/3))= 13/2(14 + 4*7)= 13/2(14 + 28)= 13/2*(42)= 13*21= 273 ans