Question

Find the sum of the first 22nd term of an ap in which d is 7 and 22nd term os 149

Answer 1

Please see the attachment

Answer 2

$\bf\huge\boxed{\boxed{\bf\huge\:Hello\:Mate}}}$

$\bf\huge Let \:a\: be\: first\: term\: be\: a\: and\: d\: be\: Common\: difference$

$\bf\huge d = 7 \:and\: a_{22} = 149$

$\bf\huge => a + (n - 1)d = 149$

$\bf\huge => a + 21\times 7 = 149$

$\bf\huge => a = 149 - 147 = 2$

$\bf\huge Substitute n = 22 , a = 2\: and\: d = 7$

$\bf\huge S_{n} = \frac{N}{2} [2a + (n - 1)d]$

$\bf\huge S_{22} = \frac{22}{2}[2\times 2 + (22 - 1)7]$

$\bf\huge = 11(4 + 21\times 7)$

$\bf\huge = 11(4 + 147)$

$\bf\huge => 11\times 151 = 1661$

$\bf\huge Sum\:of\: first\:22\:term\:is\:1661$

$\bf\huge\boxed{\boxed{\:Regards=\:Yash\:Raj}}}$