Question

Find the number of terms in each of the following APs : (i) 7, 13, 19, . . . , 205 (ii) `18 , 15 1/2, 13 , dot dot dot , - 47`

Answer 1

Let `a` is the first term, `l` is the last term,
`n` is number of terms and `d` is the common difference.

(i)Here, `a = 7, d = 6, a_n = 205`
Then, `205 = 7+(n-1)6`
`6(n-1) = 198=>n-1 = 33`
`n = 34`
So, there are `34` terms in this AP.

(ii) Here, `a = 18, d =-5/2, a_n = -47`
Then, `-47 = 18+(n-1)(-5/2)`
`5/2(n-1) = 65=>n-1 = 26`
`n = 27`
So, there are `27` terms in this AP.