Question

how many terms of ap:9,17,25.... must be taken to give their sum of 636

Answer 1

Hey !!!!

Given AP : 9 , 17 , 25

Here,

a = 9

d = 17 - 9
= 8

Sn = 636

n = ?

Therefore we know , Sn = n/2 { 2a + (n - 1)d}

=> 636 = n/2{ 2(9) + (n - 1)8}

=>1272 = n{ 18 + 8n - 8}

=>1272 = 10n + 8n²

=> 8n² + 10n - 1272 = 0

=> 4n² - 5n + 636 = 0

=> 4n² - 53n + 48n + 636 = 0

=> n(4n - 53) + 48(4n - 53) = 0

=> (4n - 53)(n + 48) = 0

=> n + 48 = 0

=> n = - 48


Since n is a natural number

=> n = 48

Hope this helps

Answer 2

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

$\bf\huge Let: first\: term\; be\: a \:and\: CD\: = 17 - 9 = 8$

$\bf\huge => S_{n} = 636$

$\bf\huge => \frac{N}{2}[2a + (n - 1)d] = 636$

$\bf\huge => \frac{N}{2}[2\times 9 + (n - 1)8] = 636$

$\bf\huge => \frac{N}{2} (8n - 10) = 636$

$\bf\huge => n(4n + 5) = 636$

$\bf\huge => 4n^2 + 5n + 636 = 0$

$\bf\huge => n = \frac{-5 + \sqrt{25 - 4\times 4\times -636}}{2\times 4}$

$\bf\huge = \frac{-5 + \sqrt{25 + 10176}}{8}$

$\bf\huge = \frac{- 5 + \sqrt{10201}}{8}$

$\bf\huge = \frac{-5 + 101}{8}$

$\bf\huge = \frac{96}{8} , \frac{-106}{8}$

$\bf\huge = 12 , \frac{-53}{4}$

$\bf\huge But\: n \:cannot\: be\: Negative$

$\bf\huge => n = 12$

$\bf\huge Hence\:Sum\: of\: 12\: terms\: is\: 636$

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