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Anastaziya [24]
3 years ago
13

F(5)= 12 for geometric sequence that is defined recursively by the formula f(n) = 0.3* f(n-1), where n is an integer and n is gr

eater than 0. Find f(7). Round your answer by the nearest hundredth
Mathematics
1 answer:
svet-max [94.6K]3 years ago
7 0

The value of f(7) is 1.08

<em><u>Solution:</u></em>

Given that,

f(5) = 12

<em><u>The sequence is defined recursively by formula:</u></em>

f(n) = 0.3 \times f(n-1)

where n is an integer and n is greater than 0

<em><u>Substitute n = 6 in given formula,</u></em>

f(6) = 0.3 \times f(6-1)\\\\f(6) = 0.3 \times f(5)\\\\Substitute\ f(5) = 12\\\\f(6) = 0.3 \times 12\\\\f(6) = 3.6

<em><u>Find f(7)</u></em>

<em><u>Substitute f = 7 in given formula</u></em>

f(7) = 0.3 \times f(7-1)\\\\f(7) = 0.3 \times f(6)\\\\f(7) = 0.3 \times 3.6\\\\f(7) = 1.08

Thus the value of f(7) is 1.08

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Step-2 : Find two factors of  -28  whose sum equals the coefficient of the middle term, which is   -12 .

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Step-5 : Add up the four terms of step 4 :

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            Which is the desired factorization

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