Complete the arithmetic sequence and then find the nth term.
__,__,6,__,15,__, 24, ...​

Given:

The arithmetic sequence is

__, __, 6, __, 15, __, 24, ...​

To find:

The missing values and the nth term of the sequence.

Solution:

The nth term of an arithmetic sequence is

        ...(1)

Where, a is the first term and d is the common difference.

3rd term of the sequence is 6.

           ...(i)

5th term of the sequence is 15

           ...(ii)

Subtracting (i) from (ii), we get

Putting d=4.5 in (i), we get

Putting a=-3 and d=4.5 in equation (1).

The nth term of the given arithmetic sequence is .

For n=1,

For n=2,

For n=4,

For n=6,

The missing values are -3, 1.5, 10.5, 19.5 respectively. So, the complete arithmetic sequence is -3, 1.5, 6, 10.5, 15, 19.5, 24, ... .

14

step-by-step explanation: