Question

Number of identical terms in the sequence $2,5,8,11,$___ upto $100$ terms and $3,5,7,9,11$____ upto $100$ terms are

• A. $17$
• B. $33$
• C. $50$
• D. $147$

Answer 1

The correct option is B $33$

Fierst series: $2,5,8,\mathrm{11.........}$

$a_1=2;d=3;n=100$

$l=20(100-1{)}^{\ast }5=2+{99}^{\ast }3=2+297=299$

so, series $=2,5,8,11,.....,197,197,200,203,....,299$

second series; $3,5,9,11,.....$

$a_1=3;d=2;n=100$

$l=3+(100-1{)}^{\ast }2=3+{99}^{\ast }2=3+198=201$

so series $=3,5,7,9,11,....,201$

series having similar terms; $5,11,17,.....,197$

$a_1=5;d=6;l=197$

$l=a_1+(n-1)d$

$197=5+(n-1)6$

$192/6=n-1$

$32+1=n$

$n=33$