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If f(1) = 7 and f(n) = -3f(n − 1) then find the value of f(6).

1 Answer

11 votes

Answer:

-1701

Explanation:

The recursion relation tells you each term of the sequence is -3 times the previous term. Then the first 6 terms are ...

7, -21, 63, -189, 567, -1701

The value of f(6) is -1701.

_____

Additional comment

The explicit formula for a geometric sequence with first term 7 and common ratio -3 is ...

f(n) = 7×(-3)^(n-1)

Then f(6) is ...

f(6) = 7×(-3)^5 = 7×(-243) = -1701

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