Question

If the nth term of 2 ap 975------ and 24,21,18,----are the same find the value of n also find that term

Answer 1

Given:   AP (1) = 9,7,5,......... and   AP(2) = 24,21,18,..........

Let a(n) be the nth term of AP(1) and a'(n) be the nth term of AP(2)

Formula for nth term of AP = a+(n-1)d,  where a is the first term, n is the number of terms and d is the difference between each term.

thus, calculating        a(n) = a+(n-1)d
                                       = 9+(n-1)(-2)
                                       = 9-2n+2
                               a(n) = 11-2n
Similarly,                a'(n)=  24+(n-1)(-3)
                                      =  24-3n+3
                               a'(n)= 27-3n

Now, as given in the question that the nth term of AP(1) and AP(2) are same
So,                       a(n)=a'(n)
                            11-2n=27-3n
                            n=16
thus value of n is 16
now calculating the value of nth term
put n=16 in either a(n) or a'(n)
                       a(n) = 11-2(n)
                              =  11-2(16)
                              =  11-32
                              =  21
so the nth term of both the APs is 21