How many terms are there in an A.P. whose first and fifth . . .

Question : How many terms are there in an A.P. whose first and fifth terms are -14 and 2 respectively and the last term is 62. [3 Marks]

CBSE 2023

Solution : 

a=-14

a₅=2

l=a_n=62

a_n=a+(n-1)d
Putting n=5
a₅=a+(5-1)d

a₅=a+4d 

2=-14+4d [∵a₅=2, a=-14]
2+14=4d
16=4d

16/4=d

4=d

d=4

Again Using 

a_n=a+(n-1)d
62=-14+(n-1)4
62+14=(n-1)4

76/4=n-1
19=n-1
19+1=n

n=20

Hence, there are 20 terms in the A.P.

Similar Question for Practice : How many terms are there in the A.P. whose first and fifth terms are -14 and 2 respectively and the sum of the terms is 40?
Ans : 10