Question

2. If 6 and 8" terms of an AP are 12 and 22 respectively, then its 29 term is
(A) 8
(B) -8
(C) 6
(D) -3​

Answer 1

a+5d = 12 a+7d = 22

From here a = -13 and d = 5

So it's 2nd term is -13 + (2-1) 5 = -8

So answer is option B

Hope it helps please mark

Answer 2

Correct Question  :

2. If 6 and 8" terms of an AP are 12 and 22 respectively, then its 2 term is

(A) 8

(B) -8

(C) 6

(D) -3​

Answer:

(B). -8

Step-by-step explanation:

n th term of an AP ,

$a_n=a+(n-1)d$

$a_6=a+(6-1)d\\\\\implies 12=a+5d\\\\\implies a+5d=12...(1)\\\\a_8=a+(8-1)d\\\\\implies 22=a+7d\\\\\implies a+7d=22...(2)$

Now substract (1) & (2) , we get ,

(a+5d)-(a+7d)=12-22

=> -2d = -10

=> d = 5

sub. d value in (1) , we get ,

=> a+5(5) = 12

=> a = 12 - 25

=> a = -13

So , 2 nd term is ,

$\implies a_{2}=a+(2-1)d\\\\\implies a_{2}=-13+(5)\\\\\implies a_{2}=-8$