Question

Two given series 2, 4, 6, 8, ......(upto 30 terms); 3,6,9,12, .... (Upto 20 terms) are in A.P.
Both of the above given series contains some terms, which are common to both of them.
7. What are the least terms of both the above given A.P?​

Answer 1

No. of terms common to both A.P = 10

The common terms of both A.P are

6,12,18 and so on . The common terms form an A.P with a common difference of 6.

The last term of the common A.P will be less or equal to the last term of both the given A.P series.

For 2,4,6,8__ till 30 terms -

Last term = 2+(29)×2

= 60

For 2,6,9,12__ till 20 terms -

Last term = 3+(19)×3

= 60

The last term of the common A.P = 60

=> 60 = 6 + (n-1)×6

=> 60 = 6n

=> n= 10

The no. of terms in the common A.P is equal to 10