Pure Year 2 Unit 3

Question 1

Formula for nth term of an arithmetic sequence

Answer 1

Un = a + (n-1)d

a is the first term and d is the common difference

Question 2

Formula for the sum of the first n terms of an arithmetic sequence

Answer 2

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

a is the first term and d is the common difference

Question 3

Formula for the nth term of a geometric sequence

Answer 3

Un = ar^(n-1)

a is the first term and r is the common ratio

Question 4

Formula for the sum of the first n terms of a geometric series

Answer 4

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

r =/= 1

a is the first term and r is the common ratio

Question 5

What is a convergent series?

Answer 5

A geometric series where modulus(r) < 1

Question 6

Formula for the sum to infinity of a convergent geometric series

Answer 6

S infinity = a/(1-r)

Question 7

Explain sigma notation

Answer 7

Greek capital letter sigma
Bottom shows the value of the variable to start on
Top shows the value of the variable to end on
Right shows the series with respect to the variable

Question 8

What does a recurrence relation do? with general rule

Answer 8

Defines each term of a sequence as a function of the previous term

For example, U n+1 = f(Un)