Arithmetic Series: Find 1st 3 Terms & 20th Term

[kwuk]

Homework Statement

The nth term of an arithmetic series is 1/2(3-n). What are the first three terms and the 20th term?

Homework Equations

nth term = a+(n-1)d

The Attempt at a Solution

I have made various attempts but cannot seem to work out how this can be done without a specific number for n. Have answered questions where two different terms have been given and used simultaneous equations to determine the first term and common difference but can't seem to do this as only one term is given. Advice anyone??

 

[tiny-tim]

The nth term of an arithmetic series is 1/2(3-n). What are the first three terms and the 20th term?

Hi kwuk!

(i assume you mean (3-n)/2)

erm … the first three terms have n = 1, 2, 3, and the 20th has n = 20

 

[Architeuthis Dux]

I would approach this problem by first understanding the concept of an arithmetic series. An arithmetic series is a sequence of numbers where the difference between any two consecutive terms is a constant value, known as the common difference. In this case, the common difference is given as 1/2(3-n).

To find the first three terms, we can substitute n=1, 2, and 3 into the given formula for the nth term. This gives us the first three terms as:

a1 = 1/2(3-1) = 1
a2 = 1/2(3-2) = 1/2
a3 = 1/2(3-3) = 0

Therefore, the first three terms of the arithmetic series are 1, 1/2, and 0.

To find the 20th term, we can use the formula for the nth term, but this time we know that n=20. So, the 20th term can be calculated as:

a20 = 1/2(3-20) = -8.5

Therefore, the 20th term of the arithmetic series is -8.5.

It is important to note that the given formula for the nth term of an arithmetic series assumes that the first term, a1, is equal to 1. If a different first term is given, the formula would be slightly different. I hope this helps to clarify the problem and provide a solution.