Question

If 6th term of an AP is -10 and its 10th term is - 26 ,then find the 15th term of an AP.
(Class 10 Maths Sample Question Paper)

Answer 1

Given :

a6 = -10, a10 = -26
nth term of an  AP : an = a +( n-1)d
a=first term , d= common Difference.
For 6th term
a6 = a +(6-1)d
a6 =a +5d
-10 = a+5d……….,...........(1)

For 10th term
a10= a+ (10-1)d
a10 = a +9d
-26 = a +9d ………………..(2)

On subtracting eq. 1 from eq. 2

-26 = a +9d
-10 = a+5d
(+)    (-) (-)
-------------------

-16 = 4d
d = -16/4 = -4
d =-4

Substitute the value of d in equation 1.

-10 = a+5d
-10 = a +5(-4)
-10 = a -20
-10+20=a
10 = a
a= 10

For finding 15 term

a15 = a + (n-1)d
a15 = 10 + (15-1)(-4)
a15 = 10 + 14 × -4
a15 = 10 -56
a15 = -46

Hence, 15 term of an AP is -46.

HOPE THIS WILL HELP YOU...

Answer 2

HELLO DEAR,


LET a is first term

and d is common difference

a6=a+(6-1)d=-10
a+5d=-10 ------------------(1)

and,
a10=a+(10-1)d=-26

a+9d=-26----------------(2)

from (1)&(2)

a+5d=-10
a+9d=-26
- - +
-------------------
-4d=16
d=-4 put in (1)


a+5*(-4)=-10
a=-10+20
a=10


a15=10+ (15-1)*(-4)

=>10-56 =-46


I HOPE ITS HELP YOU DEAR,
THANKS