Series and sequence

• Sequence- series of numbers
• arithmetic sequence- adding or subtracting a common number
• arithmetic- +/-
• geometric- x/divide
• harmonic- reciprocal of an arithmetic sequence
• fibonacci- adding the two previous numbers
• square numbers- square of a number
• cube numbers- cube of a numer: example. 1, 8, 27, 64
• common difference:  d = a(n) - a(n - 1)
• sequence= a1, a1+d, a1+2d
• general term- an= a1+(n-1)d
• an- nth term
• a1- 1st term
• (n-1) - position
• d - common difference
• formula of an arithmetic sequence- an=a1+(n-1)d
• common ratio- an/an-1
• geometric sequence formula-  an=a1(r)^(n-1)
• r- common ratio
• SUM OF FIRST NTH TERMS OF ARITHMETIC

  sn- (a1+an)n/2

  n/2 [2a1+(n-1)d]
• SUM OF INFINITE SERIES ARITHMETIC

  d>0= +infinity

  d<0= - infinity
• SUM OF FIRST NTH TERMS OF GEOMETRIC SEQUENCE- sn= a1(1-r^n/1-r)
• SUM OF INFINITE SERIES GEOMETRIC S- r<1=a1/1-r s- r>/=0 = no sum