Q) 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.

Ans: Let’s consider an A.P with first term as N1 and common difference as ‘d’.

Next, we know that n^th term of an A.P.  =  a + (n-1) d

          here, a = first term,

          n = total no. of terms till n^th term

          d = common difference between any two terms

Therefore,  1^st term, N₁ = a = -14 (given)

and  5^th term, N₅ = -14 + 4d = 2 (given)

  d = 4

Now we are given that 62 is the last term.

if 62 is the n^th term, then:

62 = -14 + (n-1) 4

n = 20

Therefore, there are 20 terms in the given A.P.