Sequences Revision 3
Arithme(c Series By Rupert
What is an Arithme(c Series? A series of numbers with a common difference and a discrete number of terms. Where [a = first term] [n = number of terms] [d=common difference] For example, in the simple series 2 4 6 8 a=2 d =2 and n=4
The Formulae If you know a, n and d then you can work out the final term in the series, and also the sum of all the numbers in the series. For the series 1 4 7 10 13……………. With 78 terms, we can apply the formula to find the final term: a+(n-‐1)d So 1 + 77x3 = 232. So the final term is 232. We could also apply the equa(on if we didn t know either a, n or d, and work backwards. For example, if we are given the sequence, but are not told that there are 78 terms, and are given the final term of 232: 1+(n-‐1)x3 =232, so (n-‐1)x3 =231, n-‐1 = 77, n=78.
nd 2 Formula To calculate the sum of the en(re series, we use the equa(on: 0.5n(2a+(n-‐1)d) So for the previous example, we simply do: 39 x (2+(77x3)) So the sum of the series = 9087 As with the last equa(on, you can also use this equa(on to solve problems by subs(tu(ng the values you do know to work out the one that you don t.
What is an Arithme(c Series? A series of numbers with a common difference and a discrete number of terms. Where [a = first term] [n = number of terms] [d=common difference] For example, in the simple series 2 4 6 8 a=2 d =2 and n=4
The Formulae If you know a, n and d then you can work out the final term in the series, and also the sum of all the numbers in the series. For the series 1 4 7 10 13……………. With 78 terms, we can apply the formula to find the final term: a+(n-‐1)d So 1 + 77x3 = 232. So the final term is 232. We could also apply the equa(on if we didn t know either a, n or d, and work backwards. For example, if we are given the sequence, but are not told that there are 78 terms, and are given the final term of 232: 1+(n-‐1)x3 =232, so (n-‐1)x3 =231, n-‐1 = 77, n=78.
nd 2 Formula To calculate the sum of the en(re series, we use the equa(on: 0.5n(2a+(n-‐1)d) So for the previous example, we simply do: 39 x (2+(77x3)) So the sum of the series = 9087 As with the last equa(on, you can also use this equa(on to solve problems by subs(tu(ng the values you do know to work out the one that you don t.
