Question

For what value of $n,$ the $n$ th terms of the sequences $3,10,17,\dots ,$ and $63,65,67,\dots .$ are equal?

Answer 1

For 1st sequence

$a=3,d=10-3=17-10=7$

$T_n=a+(n-1)d$

$T_n=3+(n-1)7$ (1)

For 2nd sequence

$a=63,d=65-63=2$

$T_n=a+(n-1)d$

$T_n=63+(n-1)2$ (2)

equate $\left(1\right)$ and $\left(2\right)$

$3+7n-7=63+2n-2$

$5n=63-2+7-3$

$5n=65$

$n=13$