Question

Find the 15th term of an Arithmetic progression whose 6th term is -10 and 10" term is​

Answer 1

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 ✅

Answer 2

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

$\bf\red{{an = a + (n - 1)d}}$

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

Final Answer :-

$\bf\red{{-46}}$