Sequences & Series

Question 1

Arithmetic sequence formula

Answer 1

Un = a + (n-1)d

Question 2

Arithmetic series formulas

Answer 2

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

Question 3

How to work out arithmetic series formula

Answer 3

Write out terms a + (a+d) + (a+2d) + … + (a+(n-1)d)
Write out terms reversed
(a+(n-1)d) + … + (a+2d) + (a+d) + a
Add them: 2Sn = n(2a + (n-1)d)
Divide by 2: Sn = n/2(2a+(n-1)d)

Question 4

Geometric sequence formula

Answer 4

Un = ar^n-1

Question 5

Geometric series formula

Answer 5

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

Question 6

How to work out geometric series formula

Answer 6

Sn = a + ar + ar^2 … ar^n-2 + ar^n-1
make another and times by r, then minus rSn from Sn
Sn - rSn = a - ar^n
Take out common factor:
Sn (1-r) = a(1-r^n)
divide by 1-r: Sn = a(1-r^n) / 1-r

Question 7

What is sum to infinity

Answer 7

S = a / 1-r

Question 8

What does divergent series mean

Answer 8

terms of series are getting larger

Question 9

What does convergent series mean

Answer 9

terms of series are getting smaller

Question 10

How to know if series is convergent

Answer 10

if |r| < 1