Find the number of terms in the finite A.P. $7, 13, 19, . . . . . . ., 151$

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Solution

Given that: $a = 7, d = T_{2} - T_{1} = 13 - 7 = 6$
Let the number of terms be n. So $T_{n} = 151$
$T_{n} = a + (n - 1) d$
$151 = 7 + (n - 1) 6 = 7 + 6 n - 6$
$151 = 1 + 6 n ∴ 150 = 6 n$
$n = \frac{150}{6} = 25 ∴ n = 25$

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A . P . 7, 13, 19, . . . ., 205

Find the number of terms in each of the following A.P.

I. 7, 13, 19, …, 205

II.

7, 13, 19, . . . ., 241

7, 13, 19, . . . .241

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