Question

Complete the recursive formula of the arithmetic sequence 12, 10, 8, 6,...12,10,8,6,...12, comma, 10, comma, 8, comma, 6, comma, point, point, point.

b(1)=b(1)=b, left parenthesis, 1, right parenthesis, equals

b(n)=b(n-1)+b(n)=b(n−1)+b, left parenthesis, n, right parenthesis, equals, b, left parenthesis, n, minus, 1, right parenthesis, plus

Answer 1

Complete Question:

Complete the recursive formula of the arithmetic sequence 12, 10, 8, 6, ....

`b_1 = [\ ]`

`b_n = b_(n - 1) + [\ ]`

Answer:

`b_1 = 12`

`b_n = b_(n-1) - 2`

Explanation:

Required

Complete:

`b_1 = [\ ]`

`b_n = b_(n - 1) + [\ ]`

From the question, the first term is 12.

So:

`b_1 = 12`

Solving further:

`b_2 = 10 = 12 - 2 = b_1 - 2`

`b_3 = 8 = 10 - 2 = b_2 - 2`

`b_4 = 6 = 8 - 2 = b_3 - 2`

Following the above sequence:

`b_n` can then be calculated as

`b_n = b_(n-1) - 2`