Question

If 19th term of an AP is47 then find the sum of 37terms

Answer 1

Let the first term be 'a'
Common difference be 'd'
$given \: \: \: t19 = 47 \\ a + (19 - 1)d = 47 \\ a + 18d = 47 - - - (1)$

$s37 = \frac{37}{2} \times (2a + (37 - 1)d) \\ = \frac{37}{2} \times (2a + 36d) \\ = 37 \times (a + 18d) \\ substituting \: \: from \: \: (1) \\ s37 = 37 \times 47 = 1739$