Question

Find the explicit form of the arithmetic function of n if the first term is 3 and the common difference is -4 . Then find the seventh term.

Answer 1

The explicit function is (b) f(n) = -4(n - 1) + 3; the seventh term is -21

How to determine the explicit form?

The given parameters are:

• First term of the sequence, a = 3
• Common difference of the sequence, d = -4

The explicit form is for an arithmetic function.

An arithmetic function has an explicit form represented as:

f(n) = a + (n -1) * d

Substitute the values of n and a in the above equation

f(n) = 3 + (n -1) * -4

Evaluate the product i.e. multiply -4 by (n - 1)

f(n) = 3 -4(n - 1)

Rewrite the equation as

f(n) = -4(n - 1) + 3

The seventh term is then calculated as:

f(n) = -4(n - 1) + 3

Substitute 7 for n in the above equation

f(7) = -4(7 - 1) + 3

Evaluate

f(7) = -21

Hence, the explicit function is (b) f(n) = -4(n - 1) + 3; the seventh term is -21

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