Question

If the 3rd term subtracted from the sum of 2nd term and 5th term gives a value equal to 10 and
the sum of second and 9th term is 17, find its first term and common difference.

Answer 1

Given, sum of second and ninth term is 17
In an A.P,
nth term = a+ (n-1)d
Therefore, second term = a+ d
And ninth term = a+8 d
3rd term = a+2d
5th term = a+4d
According to the data,
a+ d + a + 8d = 17......(1)
And a+ d + a+4d -(a+ 2d)= 10 .....(2)
By solving these two equations we get..
a+4d = 9
Substitute this value in eq(2)
We get, d= -1
On substituting this value in eq(1)
We get , a= 13