Series And Sequences

Question 1

Nth term of an arithmetic sequence

Answer 1

Un= a+(n-1)d
a= 1st term
d=common difference

Question 2

Sum of an arithmetic sequence

Answer 2

Sn= n/2 (2a+(n-1)d)

Sn=Sum of first n terms
a= 1st term
d=common difference
n=number of terms in sequence

Question 3

How to write terms of an arithmetic sequence

Answer 3

Ux= a+(x-1)d

a= first term
d=common difference
x= term

Examples:
Term 5/U5= a+4d
Term 11/U11= a+10d

Question 4

How to write terms of a geometric sequence

Answer 4

Term n/ Un= a+r^(n-1)

Term 1=a
Term 2= ar
Term 3= ar^2

Question 5

Sum of first n terms of a geometric sequence

Answer 5

Sn= a(1-r^n)/1-r
OR
Sn= a(r^n -1) /r-1

r=common ratio
a=first term
n=number of terms in sequence

Question 6

How is common ratio,r, calculated

Answer 6

2nd term/ 1st term or 3rd term/2nd term

Question 7

How is sum to infinity of a geometric series calculated and what is the rule for this

Answer 7

S ∞= a/(1-r)
Only works for a converging sequence

Infinite number of terms
a=1st term
r=common ratio

Question 8

Describe the difference between a diverging and a converging geometric series

Answer 8

Diverging series= gets bigger and bigger
Example: 2,8,32

Converging series=values get smaller and smaller and closer to a finite number therefore can be said there’s a infinite number of terms

Question 9

Sigma equation to find some of first n terms of aritmetic

Answer 9

Sn= n/2 (2a+(n-1)d)

Question 10

Describe the 2nd sigma equation for the sum of first n terms via sigma notation

Answer 10

Sn= n/2 (a+l)

a=first term
l=last term

Question 11

For sigma can split up normal eqn and x^r part

Answer 11

For sigma can split up normal eqn and x^r part

Question 12

Sigma equation for geometric

Answer 12

a(1-r^n)/1-r

Question 13

Values for which is converging

Answer 13

|x|<1

Question 14

Values for which is diverging

Answer 14

|x|>1