If-f-x-2-f-x-7-and-f-1-2-f-2-5-then-the-ratio-of-f-150-to-f-75-is-

Question Number 18859 by myintkhaing last updated on 31/Jul/17

If f (x + 2) = f (x) + 7 and f (1) = 2; f (2) = 5,

then the ratio of f (150) to f (75) is

Answered by 433 last updated on 31/Jul/17

\frac{f (150)}{f (75)} = \frac{f (2 + 2 \times 74)}{f (1 + 2 \times 37)} = \frac{f (2 + 2 \times 73 + 2)}{f (1 + 2 \times 36 + 2)} = \frac{f (2 + 2 \times 73) + 7}{f (1 + 2 \times 36) + 7} = \dots = \frac{f (2) + 74 \times 7}{f (1) + 37 \times 7} = \frac{5 + 74 \times 7}{2 + 37 \times 7}

f (x + 2 n) = f (x) + 7 n

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