The sum of all term of the arithmetic progression having ten term except for first term is 99 and except for sixth term is 89 find the third term of progression if the sum of first and fifth term is10
Ans 1:
Class : Class 10
Sum of n terms - First Term = 99 |
0.5 * n * [2a + (n-1)d] - a = 99 |
0.5 * 10 * [2a + 9d] - a = 99 |
10a + 45d - a = 99 |
9a + 45d = 99 |
a + 5d = 11 --> Eq 1
|
First Term + Fifth Term = 10 |
a + a + 4d = 10 |
2a + 4d = 10 |
a + 2d = 5 |
a = 5 - 2d --> Eq 2
|
On Substituting Eq 2 in Eq 1 |
5 - 2d + 5d = 11 |
5 + 3d = 11 |
3d = 6 |
d = 2 |
|
On Substituting d = 2 in Eq 2 |
a = 5 - 4 |
a = 1 |
|
Third term =
a + 2d =
1 + 4 =
5