What are the differences between arithmetic and geometric sequences?
An arithmetic sequence has a constant difference between each term.
For example: 2,4,6,8,10,12,…
We can see clearly that all the terms differ by +2.
We call this the common difference, d.
A geometric sequence has a constant ratio (multiplier) between each term.
An example is: 2,4,8,16,32,…
So to find the next term in the sequence we would multiply the previous term by 2.
This is called the common ratio, r.
These sequences are closely related as they both have the same first term, but I hope you can see how different they become if they have a common difference or a common ratio.
We can create a decreasing arithmetic sequence by choosing a negative common difference.
Similarly, a decreasing geometric sequence would have a common ratio of less than 1.
Related Maths GCSE answers
All answers ▸Given: 𝑓(𝑥) = 𝑎𝑥^3 + 𝑏𝑥^2 − 3 and 𝑓"(−2) = 0. If it is further given that the point (−3; 6) lies on the graph of 𝑓. Show that 𝑎 = 1/3 and 𝑏 = 2.
There are 9 counters in a bag. 7 of the counters are green. 2 of the counters are blue. Ria takes at random two counters from the bag. Work out the probability that Ria takes one counter of each colour. You must show your working.
Factorise and solve x^2-8x+15=0
Integrate x^2 + 1/ x^3 +3x +2 using limits of 1 and 0