Question

What is the explicit equation for the nth term of the arithmetic sequence 7.2, 3.8, 0.4, −3, −6.4, ...?

an = 7.2 − 3.4n
an = 7.2 + 3.4n
an = 7.2 − 3.4(n − 1)
an = 7.2 + 3.4(n + 1)

Answer 1

The explicit equation for the nth term of the arithmetic sequence is an = 7.2 + (-3.4)(n-1).

Step-by-step explanation:

The explicit equation for the nth term of an arithmetic sequence can be found using the formula: an = a1 + (n-1)d,

where an represents the nth term, a1 is the first term, and d is the common difference.

In this case, the first term (a1) is 7.2 and the common difference (d) is -3.4.

So the explicit equation for the nth term of the given arithmetic sequence is:

an = 7.2 + (-3.4)(n-1)

Answer 2

To find the explicit equation for the nth term of an arithmetic sequence, we use the formula:

an = a1 + (n-1)d

where:

an represents the nth term of the sequence

a1 represents the first term of the sequence

d represents the common difference between consecutive terms in the sequence

In this case, we can see that the first term of the sequence is 7.2, and the common difference between consecutive terms is -3.4 (we subtract 3.4 from each term to get to the next term). Therefore, we have:

an = 7.2 + (n-1)(-3.4)

Simplifying this expression gives:

an = 7.2 - 3.4n + 3.4

which can be further simplified to:

an = 10.6 - 3.4n

So the explicit equation for the nth term of the arithmetic sequence 7.2, 3.8, 0.4, −3, −6.4, ... is an = 10.6 - 3.4n.

Step-by-step explanation: