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, ... .