arithmetic sequence

• Sep 27th 2008, 09:46 AM
sameerovic
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 (Worried) and im actually from england :P
• Sep 27th 2008, 10:02 AM
civodul
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
• Sep 27th 2008, 10:03 AM
Chop Suey
Quote:

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 (Worried) 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:

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

Where \$\displaystyle a_n\$ is a term and \$\displaystyle 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:

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

(where d is the difference) to get it.
• Sep 27th 2008, 11:08 AM
ILoveMaths07
The formula for the nth term of an arithmetic sequence is given by the expression \$\displaystyle a + (n - 1) . d\$, where \$\displaystyle a\$ is the first term, \$\displaystyle n \$ is the \$\displaystyle n^{th}\$ term of the sequence, and \$\displaystyle d \$ is the common difference. Remember that \$\displaystyle d = \$ Second term \$\displaystyle -\$ First term.

You have been asked to find \$\displaystyle d\$.

\$\displaystyle d = 11 - 7 = 4. \$

You know \$\displaystyle a = 7\$.

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

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

\$\displaystyle 7 + (n - 1) . 4 \$

\$\displaystyle = 7 + 4n - 4 \$

\$\displaystyle = 4n + 3.\$

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

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

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

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

This is the same as the above sequence.

I hope that helps. :)

ILoveMaths07.