Question

How many terms of the ap 9,17,25,.. will give a sum of 636?

Answer 1

636= n/2 {2a+(n-1)d}
636=n/2{2*9+(n-1)*d}
636=n/2 *2 {9+(n-1)*4}    [taking 2 common]
636=n{9+4n-4}
636=n{5+4n}
636=5n+4n²
0=4n²+5n-636
0=4n² - 48n + 53n - 636
0=4n ( n - 12 ) + 53 ( n - 12 )
0=( n - 12 ) ( 4n + 53 )
n=12 or n=-53/4
since, negative isn't possible 
∴, 12 terms of the given A.P will give the sum 636.

Answer 2

hope it will help you