Sequences and Series

Arithmetic Sequence

100

Formula?

a_n=a₁+(n-1)d

200

The first term of an arthimetric sequence is equal to 6and the common difference is equal to 3. Find a formula for the n^th and the value of the 50^th term.

3n+3

300

The first term of an arithmetic sequence is equal to 200 and the common difference is equal to -10. Find the value of the 20^th term.

a₂₀=200+(-10)(20-10)=10

400

An arithmetic sequence has a common difference that is equal to 10 and it's 6^th term equals 52. Find the 15^th term.

a₁₅=2+10(15-1)=142

500

An arithmetic sequence has a 5^th term that is equal to 22 and its 15^th term is equal to 62. Find the 100^th term.

a₁₀₀=6+4(100-1)=402

Geometric Sequence

100

Find the terms a₂, a₃, a₄, and a₅ of a geometric sequence if a₁=10 and the common ratio is a=-1.

a₂=(a₁)r=10(-1)=-10

a₃=(a₂)r=-10(-1)=10

a₄=(a₃)r=10(-1)=-10

a₅=(a₄)r=-10(-1)=10

200

Find the 10^th term of a geometric sequence if a₁=45 and the common ration is r=0.2.

a₁₀=a₁(r^n-1)

=(45)0.2⁹=2.304(10^-5)

300

Find a₂₀ of a geometric sequence if the first few terms of the sequence are given by....

-1/2, 1/4, -1/8, 1/16

a₂₀=(a₁)r^20-1

=(-1/2)(-1/2)^20-1=1/(20²⁰)

400

Give the terms a₁₀=3/512 and a₁₅=3/16384 of a geometric sequence, find the exact value of the term a₃₀ of the sequence.

a₃₀=3(1/2)²⁹=3/536870912

500

Find a₂₀ given that a₃=1/2 and a₅=8

a₂₀=2¹⁸

Recursive Formulas

100

What does the explicit formula do.

The explicit formula designates the n^th term of the sequence, as an expression where n (n=the terms location)

Explicit Formulas

100

What does the recursive formula do?

A recursive formula designates the starting form, a₁, and the n^th term of the sequence, as an expression containing the previous term, a_n-1

Geometric Series

100

Find the sum of the first 8 terms of the geometric sequence 

3,6,12....

3,6,12,24,48,96,192,384