Arithmetic Sequences and Series




In general in arithmetic sequences, ak + 1 = ak + d.
Another name for an arithmetic sequence is an arithmetic progression (or A.P>).


Notation

• First term, a1 = a.
• Number of terms = n.
• Last term, an = l.
• Common difference = d.
• The general term, ak (the kth term).

Example: 5, 7, 8, 11, 13, 15, 17.
a = 5, l = 17, d = 2 and n = 7.

a1 = a = 5
a2 = a + d = 5 + 2 = 7
a3 = a + 2d = 5 + 2 × 2 = 9
a4 = a + 3d = 5 + 3 × 2 = 11
a3 = a + 4d = 5 + 4 × 2 = 13
a5 = a + 5d = 5 + 5 × 2 = 15
a6 = a + 6d = 5 + 6 × 2 = 17

Which can be expressed as: ak = a + (k - 1)d and for the last term becomes: l = a + (n - 1)d.


The Sum of a Series
S usually denotes the sum of a series and in Sn, n> denotes the number of terms. You can rearrange the formula l = a + (n - 1) to give n = l - a ⁄ d + 1, depending on the values you have at hand.

To work out the sum of a series, you can use the forumla S = 1 ⁄ 2 n[2a + (n - 1)d]. which can also be written as S = 1 ⁄ 2n(a + l).

Bookmark and Share