Question

In the following two A.P.'s how many terms are identical?
2,5,8,11..... to 60 terms, 3,5,7, .... 50 terms

• A. $15$
• B. $16$
• C. $17$
• D. $18$

Answer 1

Answer: (C)

$17$

$A{P}_1=2,5,8,11,14,17,21,....60termsA{P}_2=3,5,7,9,11,13,15,17,....50terms$

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 $A{P}_1$

$2,5,8,11,14,....50$

These are in AP with first term $2$ and last term $50$ and common difference $3$

Total number of terms $=n$

$n^{th}$ term $a_n=a_1+(n-1)d50=2+(n-1)348=(n-1)316=n-1n=17$

Hence, there are $17$ terms common in both APs.