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

Question

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Respuesta :

MrRoyal MrRoyal · Answer 1 · 2021-01-24T13:00:50+01:00

Complete Question:

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

[tex]b_1 = [\ ][/tex]

[tex]b_n = b_{n - 1} + [\ ][/tex]

Answer:

[tex]b_1 = 12[/tex]

[tex]b_n = b_{n-1} - 2[/tex]

Step-by-step explanation:

Required

Complete:

[tex]b_1 = [\ ][/tex]

[tex]b_n = b_{n - 1} + [\ ][/tex]

From the question, the first term is 12.

So:

[tex]b_1 = 12[/tex]

Solving further:

[tex]b_2 = 10 = 12 - 2 = b_1 - 2[/tex]

[tex]b_3 = 8 = 10 - 2 = b_2 - 2[/tex]

[tex]b_4 = 6 = 8 - 2 = b_3 - 2[/tex]

Following the above sequence:

[tex]b_n[/tex] can then be calculated as

[tex]b_n = b_{n-1} - 2[/tex]