Sequences and Series

Question 1

What is an arithmetic sequences?

Answer 1

Arithmetic sequences have common differences

Question 2

What is a geometric sequence?

Answer 2

Geometric sequences have common ratio

Question 3

What is the notation in sequences?

Answer 3

‘a’ is the first term
‘d’ is the difference between terms
‘u_n’ is the n^th term
‘n’ is the number of the term of the sequence

Question 4

What is the formula for the n^th term in an arithmetic sequence?

Answer 4

u_n = a + (n-1)d

Question 5

What are the two formulas for the sum of an arithmetic sequence?

Answer 5

S_n = n/2 * (2a + (n-1)d)

S_n = n/2 * (a + L)
Where ‘a’ is the last term

Question 6

What is the formula for the n_th term in a geometric sequence?

Answer 6

u_n = a * r^n-1

Question 7

What is the formula for the sum of a geometric sequence?

Answer 7

S_n = a(1-rⁿ) / (1-r)

Question 8

What is the formula for the sum of a geometric sequence to infinite?

Answer 8

S_INFINITE = a / 1-r
Only if geometric sequence is convergent

Question 9

What determines if a geometric sequence converges or not?

Answer 9

If ratio of geometric series is within -1 < r < 1, it is convergent