Expressions in terms of "n" for the "n"th term..? HELP?

Question

Could someone please help me with this maths question.

I can never seem to understand all this "nth" term business =S

Here are the first six terms of a number sequence

7 12 17 22 27 32

Write down an expression, in terms of n, for the nth term in this sequence.

can someone please help me work this out and explain how they did it.

thank you! :)

Answer 1

nth term just means: If you want the first term, you use n=1. If you haven't plugged in a number for n, that expression involving n gives the "nth term".

The first term is 7, and each one after it increases by a constant (5), so this is arithmetic progression.

12 - 7 = 5

Use the arithmetic progression formula:

a[sub n] = a, + d·(n - 1)

Where a, is the first term,

and d is the change between each pair of terms.

This gives:

a[sub n] = 7 + 5·(n - 1)

If you plug in 1, you get:

a, = 7 + 5·(1 - 1) = 7 + 5·(0) = 7 + 0 = 7

For n = 2:

a₂= 7 + 5·(2 - 1) = 7 + 5·(1) = 7 + 5 = 12

and so on.

So your expression of the nth term would be:

7 + 5·(n - 1)