Find the 15th term of an Arithmetic progression whose 6th term is -10 and 10" term is
Answers
QUESTION:
Find the 15th term of an Arithmetic progression whose 6th term is -10 and 10" term is -26
GIVEN:
6th term of the A.P is -10
10th term of the A.P is -26
TO FIND:
The 15th term of the A.P
SOLUTION:
We know that, in any A.P:-
an = a + (n -1)d
a6 = -10
==> a + 5d = -10 -----------(equation 1)
a10 = -26
==> a + 9d = -26 -------------(equation 2)
Subtracting equations (2) from (1), a + 5d = -10
a + 9d = -26
(2) - (1) ==> 4d = -16
==> d = -4
Common difference is -4
∴ Eqn (1) ==> a + 5(-4) = -10
==> a = -10 + 20
==> a = 10
First term of the A.P is 10
We have to find the 15th term of the A.P,
==> a15 = a + 14d
= 10 + 14(-4)
= 10 - 56
= -46
∴ 15th term of A.P is -46 ✅
Given :-
6th Term of A.p is -10
10th Term of A.p is -26
To Find :-
- The 15th Term of A.p
Solution :-
We know that in any A.p
a6 = -10
=> a + 5d = -10
=> a10 = -25
=> a + 9d = -26
Then :-
a - 5d = -10
a + 9d = -26
__________
4d = -16
__________
Then :-
d = -4
Difference = -4
=> a + 5(-4) = -10
=> a = -10 + 20
=> a = 10
First term of A.p = -10
To Find The 15th Term
=> a15 = a + 14d
=> 10 + 14(-4)
=> 10- 56
=> -46