Arithmetic Sequences
The formula for an arithmetic sequence.
What is an = a1 + (n-1)d?
Write the formula for the partial sum of an arithmetic series.
What is Sn = n ((a1 + an) / 2)?
What is the formula for the nth term of a geometric sequence?
What is an = a1 (r)n-1?
Write the formula for partial sum of a geometric series given a1 and n.
What is Sn = (a1 - a1(r)n) / (1 - r)?
The name for when an infinite sequence gets closer and closer to a finite number.
What is convergent?
Find the 20th term of the arithmetic sequence 9, 16, 23, 30,..... using the formula.
What is 142?
Find the sum of 2 + 4 + 6 + ... + 100.
What is 2550?
Find an for the geometric sequence in which a1 = 800, r = 1/2, n = 6.
What is 25?
Write the formula for partial sum of a geometric series given a1 and an.
What is Sn = (a1 - an(r)) / (1 - r)?
Write the formula for the sum of an infinite geometric series.
What is S=a1/(1-r)?
Write an equation for the nth term of the sequence where a1 = 12 and d=8.
What is an = 8n + 4?
Find the common difference d for the arithmetic sequence 3,-2, -7 ,-12,...
What is -5?
Write an equation for the nth term of the geometric sequence.
What is an = 8(1/4)n-1?
Find the sum of the geometric series in which a1 = 2000, an = 125, r = 1/2.
What is 3875?
The name given to a sequence with a common ratio with an absolute value greater than 1.
What is divergent?
Find the arithmetic means in the sequence 21, ___, ___, ___, 45,... .
What is 27, 33, 39?
Find the first three terms of the arithmetic series in which Sn = 120, n = 8, and an = 36.
What is -6, 0, 6?
Find the geometric mean of 810, ___, ___, ___, 10.
What is 270, 90, 30?
Find a20 for the geometric sequence
.01, .02, .04, .08,... cents.
What is $5242.88?
Find the sum of the infinite series if it exists.
-3 + (12/5) - (48/25) + (192/125) +...
What is -4/3?
Find the sum of the integers from 51 to 71.
What is 1281?
Find the first three terms of the arithmetic series in which a1 = 48, an = 180, and Sn = 1368.
What is 48, 60, 72?
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?
Find a1 for the geometric series in which Sn = 4118, an = 128, r = 2/3.
What is 1458?
Find the sum of the infinite series if it exists.
1 + 10 + 100 + 1000 +... .
What is a divergent series with a sum that does not exist.