For what value of n, are the nth terms of two A. Ps 63, 65, 67,.... and 3, 10, 17,.... equal?

For what value of n, are the nth terms of two A. Ps 63, 65, 67,.... an

1.	For what value of n, are the nth terms of two A. Ps 63, 65, 67,.... and 3, 10, 17,.... equal?
Answer» First APs63, 65, 67, ......Here, a = 63d = 65 - 63 = 2{tex}\\therefore {/tex}\xa0nth term = 63 + (n - 1)2\xa0{tex}\\because {/tex}\xa0an = a + (n - 1)dSecond APs3, 10, 17, .....Here, a = 3d = 10 - 3 = 7{tex}\\therefore {/tex}\xa0nth term = 3 + (n - 1)7\xa0{tex}\\because {/tex}\xa0an = a+(n - 1)dIf the n th terms of two APs are equal then63 + (n - 1)2 = 3 + (n - 1)7{tex} \\Rightarrow {/tex}\xa0(n - 1)2 - (n - 1)7 = 3 - 63{tex} \\Rightarrow {/tex}\xa0(n - 1) (2 - 7) = -60{tex} \\Rightarrow {/tex}\xa0(n - 1) (-5) = -60{tex} \\Rightarrow n - 1 = \\frac{{ - 60}}{{ - 5}}{/tex}{tex} \\Rightarrow {/tex}\xa0n - 1 = 12{tex} \\Rightarrow {/tex}\xa0n = 12 + 1{tex} \\Rightarrow {/tex}\xa0n = 13Hence, for n = 13th terms of the two APs are equal