Arithmetric And Geometric Series

Question 1

Meaning of sequences and series

Answer 1

Sequences is a set of no. arranged in a defined order

Series is the sun of the terms of a seq usually denoted by Sn

Question 2

Arithmetic Progression

Meaning
Eqn for common diff
Eqn for nth term of the AP
Eqn for Sum of 1st n terms 
Prove that a seq is an AP

Answer 2

Seq of no. For which the diff b/w 2 consecutive terms is a const

U n - U n-1 = d (common diff)

U n = a + (n-1)d

S n = n/2 (2a + (n-1) d) = n/2 (u1 + u n)

Prove that U n - U n-1 = Const
for all values of n greater or equal to 2

Question 3

Geometric Progression

Meaning
Eqn for common diff
Eqn for nth term of the GP
Eqn for Sum of 1st n terms 
Prove that a seq is an GP

Answer 3

Seq of no. for which the ratio of every 2 consecutive terms is a const

U n
——— = r (common ratio)
U n-1

U n = a r^n-1

       a (1-r^n)  S n =  ————— , r /= 1 
           1-r

         U n  Prove  ———  = const for all values of n greater or
        U n-1      equal to 2

Question 4

Sum to infinity of a geometric series

Answer 4

If |r| < 1 then n -> infinity &

         a  S∞ =  ——— , |r| < 1
       1 - r

Question 5

What does the usual a, r, d, n stand for

Answer 5

a is the first term
r is the common ratio
d is the common difference
n is the term no.

Question 6

Steps you need to show when showing sth is an arithmetic series

Answer 6

From n is more than n equal to 2,

U n = … abc…

U1 = S1 = …. = … and it follows the form Un = …abc… when n=1

Hence, U n = … abc…
for n more than and equal to 1

Question 7

For inequalities and the ans needs to be a whole no. (Eg min no.)

And u get n > 24.2

…?

Answer 7

Since n ∈ Z+, least value of n = 25

Question 8

Find the set of possible values of n for which S exceeds 4a
- how to present in sets and why ranges don’t work

How to solve for inequalities (2)
- working

Answer 8

Search for ‘for me flashcard APGP’ in famous amos WA