Sequence and Series (1)

Question 1

How to find the nth term, a numerical term or the amount of terms?

Answer 1

U_n = a + (n - 1)d

Question 2

U_n = a + (n - 1)d

Answer 2

How to find the nth term, a numerical term or the amount of terms?

Question 3

Arithmetic sequence sum when last term included?

Answer 3

S_n = (1/2)n(a + l)

Question 4

S_n = (1/2)n(a + l)

Answer 4

Arithmetic sequence sum when last term included?

Question 5

Arithmetic sequence sum when last term not included?

Answer 5

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

Question 6

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

Answer 6

Arithmetic sequence sum when last term not included?

Question 7

Find nth term, a numerical term or the amount of terms (geometric)?

Answer 7

U_n = ar^(n-1)

Question 8

U_n = ar^(n-1)

Answer 8

Find nth term, a numerical term or the amount of terms?

Question 9

Sum of geometric sequence? Where r>1

Answer 9

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

Question 10

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

Answer 10

Sum of geometric sequence? Where r>1

Question 11

Summing to infinity

Answer 11

S_infinity = a / (1 - r)

Question 12

S_infinity = a / (1 - r)

Answer 12

Summing to infinity

Question 13

Formula for nCr?

Answer 13

n! / (r! (n-r)!)

Question 14

n! / (r! (n-r)!)

Answer 14

Formula for nCr?

Question 15

Binomial Expansion formula for first 4 terms

Answer 15

1 + nx + ((n(n-1))/2!)x^2 + ((n(n-1)(n-2))/3!)x^3

Question 16

1 + nx + ((n(n-1))/2!)x^2 + ((n(n-1)(n-2))/3!)x^3

Answer 16

Binomial Expansion formula for first 4 terms

Question 17

Sum of geometric sequence? Where r<1

Answer 17

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

Question 18

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

Answer 18

Sum of geometric sequence? Where r<1

Question 19

An example of an inductive definition

Answer 19

First term: U_1=3

Recurrence relation: U_n+1 = 2u_n - 3

Question 20

The sum of the sixth to tenth terms inclusive is 30

Answer 20

S_10 - S_5 = 30