Infinities 1 sequences and series

Sequence – an ordered set of numbers or other objects

Finding the nth term Position number n Sequence Adding 3 each time

Finding the nth term of Position number 1234?n Construction from observation 1x3=32x3=63x3=94x3=12?x3=15nx3=3n Sequence ?X3+1 Observation: Add 3 each time Formula is nth term = 3n+1

Finding the nth term Position number 12345n Sequence Multiply by 2 each time

Finding the nth term Position number 12345n Sequence x2 4x14x24x44x84x16

Finding the nth term Position number 12345n Sequence x14x24x44x84x16 4x2 0 4x2 1 4x2 2 4x2 3 4x2 4 nth term = 4x2 n which can be written as...

Divergent

Convergent sequences of numbers converge to a limit number For example:

Convergent

Oscillating

Arithmetic Sequence In mathematics, an arithmetic progression (A.P.) or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, is an arithmetic progression or sequence with common difference 2.

Geometric Sequence In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54,... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25,... is a geometric sequence with common ratio 1/2.

Series - A summation of the terms in a sequence (of numbers)

reference g/mathsfit/sequencesandseries/arithmeticseq uencesandseries/ g/mathsfit/sequencesandseries/arithmeticseq uencesandseries/ g/mathsfit/sequencesandseries/geometricseq uencesandseries/ g/mathsfit/sequencesandseries/geometricseq uencesandseries/

Finding the nth term Position number 12345n Sequence Quadratic sequence so it must have form ax 2 +bx+c ax1 2 +bx1+c = 3 → a+b+c=3 ax2 2 +bx2+c = 7 → 4a+2b+c =7 ax3 2 +bx3+c = 13 → 9a+3b+c = 13 Solving you get a=1, b=1, c=1. So nth term = n 2 + n + 1