Question

Find the 54th term of the arithmetic sequence —2,-8,-14, ...

Answer 1

-320.

Explanation:

n54 = a1 + d(54 - 1)

Here a1 = -2 and d = -8 - (-2) = -6.

So 54th term = -2 + -6*53

= -320.

Answer 2

-320

Explanation:

You would first create an explicit formula for the provided sequence.

The basic explicit formula for arithmetic sequences is ,
`a_(n) = d(n-1) + a_(1)`where an is the number of the term, d is the number you are adding or subtracting by, n the location of the term, and a1 is the first number.

We would then substitute the values given.

We are trying to solve the value of the 54th term. This makes n = 54. The first number of the sequence is -2, so a1 is -2. Finally, d is -6 because we are subtracting 6 to each number in the sequence.

Therefore, our resulting equation would be
`a_(n) =-6(54-1)-2` , which equals -320.