how many terms of the AP 9,17,25.....must be taken to give a sum of 450
Answers
Answer:-
10
Step by step explanation
Given AP: 9, 17, 25......
First term, a = 9
Common Difference, d = ( a2 - a1 ) = 17 - 9 = 8
We know that the sum of n terms of an AP :-
Sn = n/2 [ 2a + ( n - 1 )*d ]
450 = n/2 [ 2 ( 9 ) + ( n - 1 )*8 ]
450 = n/2 [ 18 + 8n - 8 ]
450 = n ( 9 + 4n - 4 )
450 = 9n + 4n^2 - 4n
450 = 5n + 4n^2
4n^2 + 5n - 450 = 0
4n^2 + 45n - 40n - 450 = 0
n ( 4n + 45 ) - 10 ( 4n + 45 ) = 0
( 4n + 45 )( n - 10) = 0
n = - 45 / 4 or n = 10
Therefore there are 10 terms must be taken to a sum of 450.
( no. of terms can't be negative )
Hope it will helps you!
Answer:
Given that
9 , 17 , 25 ,....... are in A.P
First term a = 9
Common difference
d = a2 - a1 = 17 - 9 = 8
d = 8
Sum of terms in A.P
Sn = n/2 [ 2a + ( n - 1 ) d ]
450 = n/2 [ 2(9) + ( n - 1 ) 8 ]
450 = n/2 [ 18 + 8n - 8 ]
450 = n [ 9 + 8n - 8 ]
450 = 9n + 8n² - 8n
450 = 9n + 4n2 - 4n
450 = 5n + 4n²
4n² + 5n - 450 = 0
4n² + 45n - 40 - 450 = 0
n ( 4n + 45 ) - 10 ( 4n + 45 ) = 0
( 4n + 45 ) ( n - 10 ) = 0
4n + 45 = 0 | n - 10 = 0
4n = -45 | n = 10
n = -45/4 |
As the nth term cannot be negative so the 10 terms can be taken to give the sum of 450 .