Topic 3

Question 1

Formulae for Arithmetic Sequence

Answer 1

Un=a+(n-1)d

Question 2

Formulae for Arithmetic Series

Answer 2

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

Question 3

Formulae for Geometric Sequences

Answer 3

Un=ar^n-1

Question 4

Formulae for Geometric Series

Answer 4

Sn=a(1-r^n)
—————
1-r

Question 5

Formulae for sum to infinity

Answer 5

Si= a
——
1-r

Question 6

Formulae for recurrence relations

Answer 6

Un+1=F(Un)

Increasing when LHS greater
Decreasing when RHS greater
Periodic when Un+k=Un

Question 7

Prove Arithmetic Series

Answer 7

Sn=a+(a+d)+(a+2d)+……+(a+(n-2)d)+(a+(n-1)d)
Sn=Reverse

1+2:
2Sn=n(2a+(n-1)d)
Sn=n(2a+(n-1)d)
       —
       2