Question

how many term of the an A.P.9,17,25... must be taken to give a sum of 636.

Answer 1

Hi

AP : 9,17,25

a= 9
d= 17 -9 = 8
Sn = 636

we know that :

Sum= n/2[2a+(n -1) d]
put the values

636 = n/2 [2(9)+ (n - 1)8]
636 * 2 = n [ 18 +( n - 1) 8]
1272 = n [18 + 8n - 8 ]
1272 = n [10 - 8n]
1272 = 10n - 8n^2

10n + 8n^2 -1272 = 0
8n^2 + 10n - 1272 = 0
2 ( 4n^2 + 5n - 636) = 0
4n^2 + 5n - 636 = 0*2
4n ^2 + 5n - 636 = 0

Then, we solve it by quadratic formula

we know that, - b √b2 - 4ac / 2a

a = 4 , b = 5. , c = - 636

put the values

next sum see in the pic

May it is helpful for you.

Answer 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$\bf\huge => n = 12$

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

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