Question

In the following two A.P. is how many terms are identical ? 2, 5, 8, 11.........to 60 terms 3, 5, 7, 9........terms

• A. 15
• B. 16
• C. 17
• D. 18

Answer 1

Answer: (C)

$A{P}_1=2,5,8,11,14,17,21,\dots ..60$ terms
$A{P}_2=3,5,7,9,11,13,15,17,\dots .50$ terms
Since $A{P}_2$ contains less number of terms, the number of common terms is
decided by total number common of $A{P}_2$ with $A{P}_1$
From the APs we find that $2,5,8,11,..$ terms of $A{P}_2$ are common with $A{P}_1$
$2,5,8,11,14,\dots .50$
These are in $AP$ with first term 2 and last term 50 and common difference 3
Total number of terms $=n$
$n^{\text{th }}$ term $a_n=a_1+(n-1)d$
$50=2+(n-1)3$
$48=(n-1)3$
$16=n-1$
$n=17$
Hence, there are 17 terms common in both $APs$.