Question

If the third term of an A.P. is 5 and the seventh terms is 9, find the 17^th term.

Answer 1

Let the first term of an A.P. = a

And the common difference of the given A.P. = d

As, we know that,

a_n = a + (n – 1)d

∴ a₃ = a + (3 – 1)d = a + 2d

Similarly

a₇ = a + (7 – 1)d

= a + 6d

Now, we have given,

a + 2d = 5  ...(i)

And a + 6d = 9  ...(ii)

Now, Subtracting (i) from (ii); we have

        a + 6d = 9
        a + 2d = 5
       –   –      –     
`\implies`  4d = 4                 

`\implies` d = 1

Now, put the value of d in equation (i); we get

`\implies` a + 2d = 5

`\implies` a + 2 × 1 = 5

`\implies` a + 2 = 5

`\implies` a = 5 – 2

`\implies` a = 3

Now, a_n = a₁₇

= a + (n – 1)d

= 3 + (17 – 1) × 1

= 3 + 16

= 19