Question

If the first term of an arithmetic sequence is( 4)/(7) and the common difference is( 1)/(7), then find the third term using the recursive method. (4)/(49)

Answer 1

To find the third term of an arithmetic sequence, start with the first term (4/7) and add the common difference (1/7) to get the second term (5/7), and then add the common difference once more to obtain the third term (6/7).

Step-by-step explanation:

To find the third term of an arithmetic sequence using the recursive method, we need to start with the first term and then add the common difference to each consecutive term until we reach the desired term. The first term (a1) is given as (4)/(7), and the common difference (d) is given as (1)/(7).

To find the second term (a2), we simply add the common difference to the first term:

a2 = a1 + d = (4)/(7) +(1)/(7) = (5)/(7)

Now, to find the third term (a3), we again add the common difference to the second term:

a3 = a2 + d = (5)/(7) + (1)/(7) = (6)/(7)

Therefore, the third term in this arithmetic sequence is (6)/(7).