Question

Show that the sequence 9, 12, 15,18 is an AP. Find it's 16th term and the general term ?

Answer 1

Hi,

Here is your answer,

Given,

           a(First term) = 9, d(common difference) 12 - 9 = 3 

Formula:- an = a+(n-1)d

      an  =   9+(n-1)3

       an = 9 + 3n - 3

        an = 6 + 3n


Now, 16th term of an A.P,

                a₁₆ = 6 + 3 × 16

                 a₁₆   = 6 + 48

                  a₁₆  = 54


Therefore the 16th term of an A.P is 54.



Hope it helps you !

Answer 2

Given,

A sequence 9, 12, 15, 18

To Find,

Whether the sequence is A.P or not and the 16th and general term.

Solution,

The given sequence is 9, 12, 15, 18

d = 12-9 = 15-12 = 3

Since the common difference between each term is the same. So the given sequence is an A.P.

So,

a₁₆ = a+15d

a₁₆ = 9+15*3

a₁₆ = 9+45 = 54

Now,

aₙ = a+(n-1)d

aₙ = 9+(n-1)3

aₙ = 9+3n-3

aₙ = 6+3n

Hence, the 16th term of the A.P is 54 and the nth term is 6+3n.