Question

The number of terms common between the two series 2 + 5 + 8 + …up to 50 terms and the series 3 + 5 + 7 + 9 + ….up to 60 terms.

• A. 24
• B. 26
• C. 25
• D. None of these

Answer 1

The correct option is D None of these

Let $m^{th}$ term of first A.P. be equal to the $n^{th}$ term of the second A.P. then
2 , 5 , 8 ,….50 terms series 1
3 , 5 ,7 , …., 60 terms series 2
Common series 5 , 11, 17 , ….., 119
${40}^{th}$ term of series $1={59}^{th}$ term of series 2 = 119 = last term of common series
$\Rightarrow a_n=5+(n-1)d\Rightarrow 119+1=6n\Rightarrow n=20.$
$\therefore$ Number of common terms is 20.