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given the formula for an arithmetic sequence f(7) = f(6) + 4 written using a recursive formula, write the sequence using an arithmetic formula.

f(7) = f(1) + 24
f(7) = f(1) + 20
f(7) = f(1) + 12
f(7) = f(1) + 4

f(7) = f(1) + 24

Step-by-step explanation:

from f(7) = f(6) + 4

we can observe that any term is basically the previous term in the progression plus 4 which means:

f(6) = f(5) + 4

f(5) = f(4) + 4

f(4) = f(3) + 4

f(3) = f(2) + 4

f(2) = f(1) + 4

If we start substituting the lower terms into next highest term, starting from the bottom and working our way up, we will get:

f(3) = f(2) + 4 = [ f(1) + 4 ] + 4 = f(1) + 8

f(4) = f(3) + 4 = f(1) + 8 + 4 = f(1) + 12

f(5) = f(4) + 4 = f(1) + 12 + 4 = f(1) +16

f(6) = f(5) + 4 = f(1) + 16 + 4 = f(1) + 20

f(7) = f(6) + 4 = f(1) + 20 + 4 = f(1) + 24