What term of the arithmetic sequence is the given number

Asked by admin @ 26/11/2021 in Mathematics viewed by 331 People

Consider the arithmetic sequence:

10, 12, 14, 16, ...
If n is an integer, which of these functions generate the sequence?
Choose all answers that apply:
A a(n) = 16+ 3n for n > -2
b(n) = 14 + 2n for n > -1
c(n) = 10 + 3n for n > 0
D
d(n) = 8 + 2n forn > 1

Answered by admin @ 26/11/2021

Answer:

Answer: D

Step-by-step explanation:

Arithmetic Sequences

The arithmetic sequences are those where any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

$a_n=a_1+(n-1)r$

Where

an = nth term

a1 = first term

r = common difference

n = number of the term

We are given the arithmetic sequence:

10, 12, 14, 16, ...

Where a1=10 and

r = 12 - 10 = 2

Thus the general term is:

$a_n=10+(n-1)2$

Operating:

$a_n=10+2n-2$

$a_n=8+2n$

Answer: D

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