How many terms are there in the sequence $4, 11, . . . . . . ., 298$ ?

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Solution

Given series is $4, 11, . . . . . ., 298$
$a_{n} = a + (n - 1) d$
Here $a = 4, a_{n} = 298, d = 7$
$298 = 4 + (n - 1) 7$
$298 = 4 + 7 n - 7$
$7 n = 301$
$∴ n = 43$

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