Arithmetic Sequences
The formula for an arithmetic sequence.
What is an = a1 + d(n-1)
Write the formula for the sum of a finite arithmetic series.
What is Sn= n/2(a1+an)
What is the formula for the nth term of a geometric sequence?
What is an = a1(r)^(n-1)
What is the sum of the following geometric series.
a1= 1, r = 5, n = 7
What is 19531.
Write in sigma notation: 1+2+3+...25
What is ∑_(n =1)^25〖n〗
top: 25
function: n
bottom: n = 1
Find the 40th term of the arithmetic sequence 9, 16, 23, 30,..... using the formula.
What is 282.
Find the sum of the first 50 even numbers.
2 + 4 + 6 + .... + 100.
What is 2550.
Find a6 for the geometric sequence in which a1 = 800, r = 1/2, n = 6.
What is 25.
Find the sum of the geometric series: 2 + 6 + 18 + 54 + 162 + 486 + 1458.
What is 2186.
Write the summation notation for the following arithmetic sequence.
4 + 7 + 10 + 13 +16 + 19
∑6n=1(4+3(n-1))
or
∑6n=1(3n+1)
Write an equation for the nth term of the sequence where a1 = 12 and d=8.
What is an = 8n + 4 or an = 12 +8(n-1)
Find the number of terms in an arithmetic series in which A1 = 48, An = 180, and Sn = 1368.
What is 12.
Write an equation for the nth term of the following geometric sequence.
8, 6, 9/2, ...
What is an = 8(3/4)^n-1
Find the sum of the geometric series in which A1 = 2000, An = 125, r = 1/2.
What is 3875.
Write out ∑11(n=5)〖3-2n〗
-7-9-11-13-15-17-19
Find the common difference of the following arithmetic sequence 21, ___, ___, ___, 45,......
What is 6.
Find the first term of the arithmetic series in which Sn = 120, n = 8, and a8 = 36.
What is -6.
Find the common ratio of this geometric sequence of 810, ___, ___, ___, 10.
What is 1/3.
Find a1 for the geometric series in which S4 = 4118 & r = 2/3.
Round answer to the nearest hundredth.
1710.55
Write 3+6+12+...3072 in sigma notation.
What is ∑11n=1〖3*2^(n-1)〗
Joe averaged 123 total pins per game in his bowling league this season. He is taking bowling lessons and hopes to bring his average up by 8 pins each new season. What will Joe's average be on game 12?
What is an = 8n + 115 or an = 123 + 8(n-1)
Find the sum of the following arithmetic series.
The last term is a34= 17 and the common difference is -4.
What is 2822.
Sarah receives a joke in an E-mail that asks her to forward it on to four of her friends. She forwards it, then each of her friends forwards it to four of their friends, and so on. If the pattern continues, how many people will receive the E-mail on the ninth round of forwarding?
What is 262,144.
On this first round of forwarding 4 people get it so a1 is 4, on the ninth round of forwarding we are looking for a9.
a9 = 4(4)^(9-1)
Write a geometric series with 5 terms such that the sum of the series is 100.
(Hint: Chose a value of r and then find a1)
Answers will vary
Evaluate the following sum ∑11(x=1)〖3(-2)^(n-1)〗
(give me the sum, not necessarily the expanded form)
What is 2049.