Given the functions f(n) = 11 and g(n) = −2(n − 1), combine them to create an arithmetic sequence, an, and solve for the 31st term.

Answer:

Refer below for the explanation.

Step-by-step explanation:

As per the question we are asked to combine f(n) = 11 and g(n) = −2(n − 1), both of them to create arithmetic sequence and solve for 31st term.

So first we are about to solve and combine both of the equation which becomes ,

Fn = 11 -2(n-1)

Fn=11-2(n-1)

F31=-49

Fn=11-2(n-1)

F31=-51

Fn=11+2(n-1)

F31=71

Fn=11+2(n-1)

F31=73

Final answer:

To create an arithmetic sequence using the given functions, we add the functions together and substitute the desired term. The 31st term of the arithmetic sequence is -49.

Explanation:

To combine the functions f(n) = 11 and g(n) = -2(n - 1) into an arithmetic sequence, we need to find the common difference between the terms. The common difference between the terms in an arithmetic sequence is obtained by subtracting one term from the previous term. In this case, the common difference is g(n). So, the arithmetic sequence can be expressed as an = f(n) + g(n).

For the 31st term, we substitute n = 31 into the equation and calculate:

a31 = f(31) + g(31)

a31 = 11 + [-2(31 - 1)]

a31 = 11 + [-2(30)]

a31 = 11 + [-60]

a31 = -49

Therefore, the 31st term of the arithmetic sequence an is -49.

Learn more about Arithmetic Sequences here:

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