Question

13. If t, represents nth term of an A.P., t2
+ t5 - t3 = 10 and t2 + t9 , = 17, find its
first term and its common difference.
Chapter- Arithmetic Progression

Answer 1

t

2

+t

5

−t

3

=10

Let the first term be a and common difference =d

⇒t

n

=a+(n−1)d

t

2

+t

5

−t

3

=10

(a+d)+(a+4d)−(a+2d)=10

a+3d=10.............(1)

also,

⇒t

2

+t

9

=17

a+d+a+8d=17

2a+9d=17............(2)

By (1)×2−(3)

⇒−3d=3

d=−1

a−3=10

⇒a=13

∴ First term =13 Common difference =−1.

Hence, the answer is 13,−1.