P2.3 Sequences & Series

Question 1

what is the common difference in arithmetic sequences?

Answer 1

constant

Question 2

what is the formula for nth term of arithmetic sequence?

Answer 2

Un = a + (n-1)d

Question 3

what is the sum of the first n terms of an arithmetic series?

Answer 3

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

Sn = n/2 (a+l)

Question 4

what is the method to prove the sum of the first n terms of an arithmetic sequence?

Answer 4

1. write out the sum of the terms
   Sn = a + (a+d) + (a+2d)…(a+(n-2)d) + (a+(n-1)d)
2. write out the sum reversed
   Sn = (a+(n-1)d) + (a+(n-2)d) + (a+2d) + (a+d) + a
3. add together & divide by 2
   2Sn = n(2a + (n-1)d)
   Sn = n/2 (2a + (n-1)d)

Question 5

what is a geometric sequence?

Answer 5

common ratio b/w consecutive terms

Question 6

what is the formula for the nth term of a geometric sequence?

Answer 6

Un = ar^(n-1)
using logs to find n

Question 7

what is the formula for the sum of the first n terms of a geometric series?

Answer 7

Sn = a(1-r^n) / 1-r r<1
Sn = a(r^n-1) / r-1 r>1

Question 8

what is the proof for the formula for the sum of the first n terms of a geometric series?

Answer 8

see OneNote

Question 9

what happens when r is -ve?

Answer 9

it creates an alternating sequence

Question 10

what is true for r in a convergent sequence?

Answer 10

modulus r < 1