Question

The third and eighth terms of an A.P. are 14 and -26
Which term of the A.P. is -106?​

Answer 1

Answer:

18 th term

Step-by-step explanation:

3rd term of AP can be written as a+2d = 14

and 8th term is a+7d = -26

a+2d - (a+7d) = 14 -(-26)

-5d = 40

d = -8

a+2d = 14

a = 14 -2(-8)

a = 14 + 16

a = 30

now , a+(n-1)d = -106

30 + ( n-1 ) -8 = -106

n-1 = -106 -30 / -8

n-1 = -136 / -8

n-1 = 17

n = 18

18th term is -106

Answer 2

Answer:

18th term

Step-by-step explanation:

$a_{n} = a + (n - 1)d$

Third term is 14

So, 14 = a + (3-1)d

or, 14 = a + 2d

a = 14 - 2d

Eighth term is -26

So, -26 = a + (8-1)d

or, -26 = a + 7d

-26 = 14 -2d +7d = 14 + 5d

5d = -26 -14 = -40

Thus, d = -8

Therefore, the first term, a = 14 - 2×(-8)

a = 14 + 16 = 30

Now, -106 = 30 + (n-1) × (-8)

-106 - 30 = -8 (n-1)

-136 = -8 (n-1)

n-1 = 136/8 = 17

n = 17 + 1 = 18

Therefore, -106 is the 18th term of the AP.