Question

Following two given series are in A.P.

$2,4,6,8...$$3,6,9,12...$

First series contains $30$ terms, while the second series contains $20$ terms. Both of the above given series contains some terms, which are common to both of them.The last term of both the above given A.P. are

• A. $57$
• B. $60$
• C. $50$
• D. $54$

Answer 1

The correct option is B $60$

The last term of first A.P. with first term as $2$, common difference as $2$ and number of terms as $30$ will be
$t_{30}=2+(30-1)\times 2$
$t_{30}=2+29\times 2$
$t_{30}=2+58$
$t_{30}=60$
The last term of second A.P. with first term as $3$, common difference as $3$ and number of terms as $20$ will be
$t_{20}=3+(20-1)\times 3$
$t_{20}=3+19\times 3$
$t_{20}=3+57$
$t_{20}=60$