Question

In the following two AP's how many terms are identical ?

2 , 5 , 8 , 11 , ....... to 60 terms ,
3 , 5 , 7 , ........ to 50 terms


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⭐Answer with step-by-step explanation.. ​

Answer 1

The answer is given below.

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Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

$AP_{1}$=2,5,8,11,14,17..............to 60 terms

$AP_{2}$=3,5,7,9,11,13,15,17............to 50 terms

60th term =a+59d=>$2+59\times3=179$

50th term =a+49d=>$3+49\times2=101$

Since,common terms in both APs are 5,11,17......101

Here,a=5 ,$a_{2}=11$

D=$\bold{\green{a_{2}-a}}$

D=11-5=6

Last term $a_{n}=101$

$\bold{\boxed{\purple{a_{n}=a+(n-1)d}}}$

$= > 101 = 5 + (n - 1)6$

$= > 101 = 5 + 6n - 6$

$= > 101 = 6n - 1$

$= > 102 = 6n$

$= > n = \frac{102}{6} = 17$

$\bold{\boxed{\red{n = 17th \: term}}}$

$\therefore$There are 17 terms identical.