Question

the 7th term of an A.P. is 40 and its 13th term is 80. find the sum of its first 19 terms​

Answer 1

Answer:

Sum of first 19 terms =114

Step-by-step explanation:

Let the first term be a and common difference be d.

7th term = a+6d= 40

a=40-6d  - eqn (1)

13th term = a+12d=80

from eqn (1), we have:

40-6d+12d=80

6d=40

d=20/3

Thus, from eqn (1), a = 40-6(20/3) = 40-40=0

Sum of first n terms = n/2 [2a+(n-1)d]

Thus, Sum of it's first 19 terms = 19/2 [2(0) +18(20/3)] = 19/2 [0+120] = 114

Sum of it's first 19 terms =114