Basic Sequences and Series
What does a1 mean?
The first term
What are the two pieces of a recursive formula?
The base case/term and the rule involving an-1.
What does d stand for?
The common difference.
How do we find r?
a2 ÷ a1
Evaluate the arithmetic series
2+5+8+11+14+17+20
77
Find the first three terms of the sequence.
an= 6n-7
-1, 5, 11
a1= 5
an= an-1 - 2
5, 3, 1, -1, -3
Find d of the following sequence.
870, 750, 630, 510
d = -120
Find r of the following series
2, 14, 98, 686
r = 7
Evaluate the following geometric series
-2 -10 -50 -250 ... S7
-26042
Find the next three terms of the sequence
25, 34, 43, 52,...
61, 70, 79
Find the 4th term if the sequence.
a1= 6
an= an-1+11
a4=39
Find the explicit formula for the following sequence.
14, 11, 8, ...
an= -3n + 17
Find r of the following series
8, 20, 50, 125
r = 5/2
Evaluate the following Geometric series.
40, -20, 10, ...
80/3
26.6666666666666667
Find a18 of the following sequence.
an = 5 - 8n
-139
Find the Recursive formula of the following sequence.
-16, -11, -6, -1
a1= -16
an= an-1 + 5
Find the 21st, 22nd, and 23rd term of the following sequence.
-10, -14, -18, -22
-90, -94, -98
Write the formula for the following geometric sequence.
162, 108, 72, 48, ...
an= 162(2/3)n-1
Lee earned $240 in the first week, $350 in the second week and $460 in the third week, and so on in an arithmetic sequence. How much did he earn in the first 6 weeks?
Write the series in sigma notation.
5+6+7+8+9+10
answer on board
Find the recursive formula of the following sequence.
2, 5, 11, 23, ...
a1 = 2
an = 2an-1+1
Find the explicit formula of the following sequence.
-4, 1, 6, 11, ...
an = 5n - 9
Write the explicit formula for the following geometric sequence.
7, -7, 7, -7, ...
an= 7(-1)n-1
Evaluate the following geometric series.
64, 80, 100, 125
This series diverges.
This is not possible. r = 5/4