what is the nth term for the following sequence which begins
7, 11, 15, 19, 23
Is this an arithmetic progression (AP) or geometric progression (GP)?
AP's have constant differences, while GP's have constant ratios.
Given series:
7, 11, 15, 19, 23
differences:
11-7=4, 15-11=4, 19-15=4, 23-19=4
(constant difference d=4, therefore AP)
ratios:
11/7, 15/11, 19/15, 23/19 (different, so NOT GP).
The nth term of an AP is:
A(n)=A(1)+(n-1)d
d=4
A(n)=A(1)+(n-1)d
=7+(n-1)4
=7+4n-4
=3+4n
it just says work out the nth term for the those numbers
I hope you did not just read the first line of my response.
I was asking myself that question (hope you do the same). The rest of the response followed.
To find the nth term of a sequence, we need to identify the pattern or rule that governs the sequence. Looking at the given sequence:
7, 11, 15, 19, 23
We can observe that each term is obtained by adding 4 to the previous term. Therefore, the pattern or rule for this sequence is to add 4 to the previous term to get the next term.
Using this pattern, we can generate the sequence:
7 + 4 = 11
11 + 4 = 15
15 + 4 = 19
19 + 4 = 23
So, to find the nth term of this sequence, we can use the formula:
nth term = first term + (n - 1) * common difference
In this case, the first term (a) is 7, and the common difference (d) is 4.
Therefore, the nth term is given by:
nth term = 7 + (n - 1) * 4
Simplifying this equation gives us the formula:
nth term = 4n + 3
So, the nth term for the given sequence 7, 11, 15, 19, 23 is 4n + 3.