# Math Help - arithmetic sequence

1. ## arithmetic sequence

well it gives me a sequence 7,11,15,19 and say calculate the difference between the successive term then asks to determine the formula that generates the sequence. any idea on how to do it or an easy explanation for a 14 yr old boy and im actually from england :P

2. You have a sequence, this means an ordered list of numbers

Let us call the first U1, the second U2, the third U3, the fourth U4 and so one. The Nth one will be UN.

Here you have: U1=7 U2=11 U3=15 U4=19

U2-U1=4
U3-U2=4
U4-U3=4

And so more generally: UN-UN-1= 4
which can be written: UN=UN-1+ 4

And this is the formula that generates the sequence. This kind of sequence has an important role in mathematics and in practical life.

Civodul

3. Originally Posted by sameerovic
well it gives me a sequence 7,11,15,19 and say calculate the difference between the successive term then asks to determine the formula that generates the sequence. any idea on how to do it or an easy explanation for a 14 yr old boy and im actually from england :P
"7,11,15,19" is an arithmetic series, which means there is a constant common difference between each consecutive terms of the sequence.

The difference can be found by:

$d = a_{n+1} - a_{n}$

Where $a_n$ is a term and $a_{n+1}$ is the term that succeeds it.

They then ask you for an explicit formula for this sequence. Simply use the following equation:

$t_n = t_1 + (n-1)(d)$

(where d is the difference) to get it.

4. The formula for the nth term of an arithmetic sequence is given by the expression $a + (n - 1) . d$, where $a$ is the first term, $n$ is the $n^{th}$ term of the sequence, and $d$ is the common difference. Remember that $d =$ Second term $-$ First term.

You have been asked to find $d$.

$d = 11 - 7 = 4.$

You know $a = 7$.

Don't plug in anything for $n$! Without $n$, the formula will be a pure number!

So $a + (n - 1) . d$ becomes

$7 + (n - 1) . 4$

$= 7 + 4n - 4$

$= 4n + 3.$

To check your answer, plug in different values for $n$:

When $n = 1$, the first term is $7$.

When $n = 2$, the second term is $11$.

When $n = 3$, the third term is $15$.

When $n = 4$, the fourth term is $19$.

This is the same as the above sequence.

I hope that helps.

ILoveMaths07.