An A.P. is given by k,2k/3,k/3, 0,...
Find the 6th term.
To find the 6th term of the arithmetic progression (A.P.), we'll make use of the given terms.
The sequence is given by k, 2k/3, k/3, 0, ...
To determine the 6th term, we need to examine the pattern of the sequence and find the common difference (d).
Looking at the given terms, we can observe that each term is obtained by subtracting the previous term by d.
From k to 2k/3, we can see that the common difference is k/3.
Going from 2k/3 to k/3, the common difference remains k/3.
Lastly, from k/3 to 0, the common difference is also k/3.
Since we have established that the common difference (d) is constant, we can calculate the 6th term as follows:
6th term = 1st term + (n - 1) * d
Here, the 1st term (a) is k, the common difference (d) is k/3, and the term number (n) is 6.
Plugging in the values, we can calculate the 6th term:
6th term = k + (6 - 1) * (k/3)
= k + 5k/3
= (3k + 5k) / 3
= 8k / 3
Therefore, the 6th term of the arithmetic progression is 8k/3.
if AP , then
d = 2k/3 - k
= 2k/3 - 3k/3 = -k/3
term 6 = a+5d
= k + 5(-k/3) = -2k/3