The common difference of the A . P . b 1 , b 2 , . . . . , b m is 2 more than common difference of A . P . a 1 , a 2 , . . . . . , a n . If a 40 = - 159 , a 100 = - 399 and b 100 = a 70 , then b 1 is equal to :

Step-by-step solution

Let a 1 , a 1 + d 1 , a 1 + 2 d . . . . . . . . . . . . . . . . . first A . P . a 40 = a 1 + 39 d = - 159 .....................(1) a 100 = a 1 + 99 d = - 399 ....................(2) d = - 4 , a 1 = - 3 now b 100 = a 70 ⇒ b 1 + 99 D = a 1 + 69 d b 1 + 99 ( - 2 ) = - 3 + 69 ( - 4 ) ( ∵ Accoding to question D = d + 2 ) ⇒ b 1 = - 81