First, obviously, you have to stare at the five terms that you're given, and try
to figure out what's going on here ... what rule is generating those terms. Then,
once you've spotted the rule, you have to write an algebraic expression for it.
I stared at this thing for a few minutes, and finally understood what's going on:
The sequence is just a list of the squares of the counting numbers, but for each
even counting number, the term of the sequence is negative.
So the algebraic expression for the rule needs two parts: One part that produces
the square of 'n', and another part that makes the term negative if 'n' is an even
number.
Can you do that now ?
What I came up with is:
The 'n'th term of the sequence is (-1)(n+1) times n2
You see, (-1)(n+1) is just ' 1 ' when 'n' is odd, and ' -1 ' when 'n' is even.
It is: nth term = 35-9n
multiplies by 2
No, it will be a formula, because "the nth term" means that you have not defined exactly which term it is. So, you make a formula which works for ANY term in the sequence.
There is no formula for prime numbers. They form a random sequence.
Depends on the sequence. There may be a formula for the Nth term in which case it is easy. Or the value may depend on some combination of previous terms (as in the Fibbonaci series).
Find the formula of it.
The given sequence is an arithmetic sequence with a common difference of 6. To find the nth term of this sequence, we can use the following formula: nth term = first term + (n - 1) x common difference where n is the position of the term we want to find. In this sequence, the first term is 1 and the common difference is 6. Substituting these values into the formula, we get: nth term = 1 + (n - 1) x 6 nth term = 1 + 6n - 6 nth term = 6n - 5 Therefore, the nth term of the sequence 1, 7, 13, 19 is given by the formula 6n - 5.
the first 4 terms of the sequence which has the nth term is a sequence of numbers that that goe together eg. 8,12,16,20,24 the nth term would be 4n+4
It is: nth term = 35-9n
multiplies by 2
The nth term of the sequence is expressed by the formula 8n - 4.
The nth term is: 5-6n
No, it will be a formula, because "the nth term" means that you have not defined exactly which term it is. So, you make a formula which works for ANY term in the sequence.
8
The nth term of a sequence is the general formula for a sequence. The nth term of this particular sequence would be n+3. This is because each step in the sequence is plus 3 higher than the previous step.
Give the simple formula for the nth term of the following arithmetic sequence. Your answer will be of the form an + b.12, 16, 20, 24, 28, ...
There is no formula for prime numbers. They form a random sequence.