The 10th common term between the series 3+7+11+ . . . And 1+6+11+ . . . ., is

Options

A. 189
B. 191
C. 211
D. 213

Answer

B

Explanation

Series `3+7+11+"…"` has common difference =4 and series `1+6+11+"…"` has common difference =5
Hence, the series with common trms has common difference LCM of 4 and 5 which is 20.
The first common terms is 11.
Hence, the series is `11+31+51+71+"..."`
`:. t_(10)=11+(10-1)(20)=191`
Aliter `t_(n)` for `3+7+11+"..."=3+(n-1)(4)=4n-1`
and `t_(m)` for `1+6+11+"..."=1+(m-1)(5)=5m-4`
For a ommon term, `4n-1=5m-4 i.e., 4n=5m-3`
For `m=3,n=3` gives the first common term `i.e.,11.`
For `m=7,n=8` gives the second term `i.e.,31`.
For `m=11,n=13` gived the third common term i.e., 51.
Hence, the common term series is `11+31+51+"..."`
`:. t_(10)=11+(10-1)20=191`