Question

In an ap if a2 + a5 - a3=10 and a2 +a9 = 17 find the ap

Answer 1

Answer:

13,12,11,10,.....

Step-by-step explanation:

Let first term=a

and, common difference=d

formula : nth term = a+(n-1) d

Given, a2 + a5 - a3=10

or, (a+d) +(a+4d)-(a+2d)=10

or, a+3d=10...... (i)

and, a2 +a9 = 17

or, (a+d) +(a+8d) =17

or, 2a+9d=17......(ii)

multipying equation (i) by 2 then subtracting by equation (ii), we get

9d-6d=17-20

or, 3d=-3

or, d=-1

putting d=-1 in equation (i), we get

a+3(-1)=10

or, a=10+3=13

therefore, the AP is given by

13,12,11,10,......