Find the number of common terms to the two sequences 17, 21, 25, 417 and 16, 21, 26, .., 466.

Options

A. 21
B. 19
C. 20
D. 91

Answer

C

Explanation

Let `m^(th)` term of the first sequence be equal to the n `n^(th)` term of the second sequence. Then,
`17+4(m-1)=16+5(n-1)`
`rArr" "4m=13-5n+11`
`rArr" "4m+2=5n`
`rArr" "n=m-(1//5)(m-2)`
Since n is an integer m-2 must be a multiple of 5, i.e., m must be of the form 5k+2, with `kgt0`. Then, `n=4k+2`.
The first sequence has 101 terms and the second has 91 terms.
`:." "0le5k+2lt101and0le4k+2le91`
`rArr" "=0lekle19`.
Hence, the given sequences have 20 common terms.