Question

Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1?


6, 1, –4, –9, –14, …


f (n + 1) = f(n) + 5

f (n + 1) = f(n) – 5

f (n) = f(n + 1 ) – 5

f (n + 1) = –5f(n)



The Answer is f (n + 1) = f(n) – 5

Answer 1

Please see the attachment

Answer 2

The recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1 is  f(n + 1) = f(n) – 5

Solution:

Given the sequence is:

6 , 1 , - 4 , -9 , -14 , ....

Analyse the given sequence and find the pattern followed

$First\ term = 6 \\\\Second\ term = 6 - 5 = 1 \\\\Third\ term = 1 - 5 = -4 \\\\Fourth\ term = -4 - 5 = -9 \\\\Fifth\ term = -9 - 5 = -14 \\\\And\ so\ on$

Thus we can see successive terms are found by subtracting 5 from previous terms

Which can be written as:

$f(n + 1) = f(n) - 5$

Where, "n" is the terms location

f(1) = 6 , $n \geq 1$

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