Question

Identify the recursive formula for the sequence 20, 28, 36, 44,.

Answer 1

Answer:

C.

$f_n = \left \{ {{f_1=20} \atop {f_n=f_{(n-1)} + 8}; n>1} \right.$

Step-by-step explanation:

Given:

Sequence: 20, 28, 36, 44,

Required

Find the recursive formula

Let $f_1$ represents the first term

$f_1 = 20$

Representing the other terms in terms of the previous terms

$f_2 = 28\\f_2 = 20 +8\\f_2 = f_1 + 8$

$f_3 = 36\\f_3 = 28 + 8\\f_3 = f_2 + 8$

$f_4 = 44\\f_4 = 36 + 8\\f_4 = f_3 + 8$

Bringing them together, we have

$f_1 = 20\\f_2 = f_1 + 8\\f_3 = f_2 + 8\\f_4 = f_3 + 8$

$f_1 = 20\\f_2 = f_{2-1} + 8\\f_3 = f_{3-1} + 8\\f_4 = f_{4-1} + 8$

Replace each term with n

$f_1 = 20\\f_n = f_{n-1} + 8\\f_n = f_{n-1} + 8\\f_n = f_{n-1} + 8\\Where\\n > 1$

Delete repetition

$f_1 = 20\\f_n = f_{n-1} + 8\\Where\\n > 1$

So, the recursive formula is:

$f_n = \left \{ {{f_1=20} \atop {f_n=f_{(n-1)} + 8}; n>1} \right.$