9.4 Summer School Day 2
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9.4 Sequences and Series continued
Title: Jul 206:54 AM (1 of 20)
The average of three successive terms of an arithmetic sequence is 47.2. What is the second of the three terms?
Title: Jul 216:58 AM (2 of 20)
The first term of an arithmetic sequence is 325, and the 82nd term is 352. Find the common difference and the sum of the 12th through the 82nd terms.
Title: Jul 216:59 AM (3 of 20)
The sum of two consecutive terms of an arithmetic sequence is 2. Their product is -24. The first of the two terms is smaller than the second. Find the two terms.
Title: Jul 217:00 AM (4 of 20)
The first term of an arithmetic series is 2 and the common difference is 3. The sum is 187. How many terms are in the series?
Title: Jul 217:12 AM (5 of 20)
The 452nd term of an arithmetic sequence is -893 and the 84th is 27. Find the first five terms of the sequence.
Title: Jul 217:05 AM (6 of 20)
Suppose that at the beginning of the year, your savings account contains $4250. If you withdraw $350 per month from the account, how much will it contain at the end of the year.
Title: Jul 217:06 AM (7 of 20)
The lengths of the sides of a right triangle form an arithmetic sequence with common difference 3. Find the lengths of the sides.
Title: Jul 217:14 AM (8 of 20)
Formula for Geometric Series
Title: Jul 207:12 AM (9 of 20)
Find the sum of the geometric sequence 4, -4/3, 4/9, -4/27, …, 4(-1/3) 10.
Title: Jul 207:19 AM (10 of 20)
Linda deposits $250 at the end of each month into an account that pays 3% interest compounded monthly. After 10 years, the balance in the account is
Find her balance.
Title: Jul 207:19 AM (11 of 20)
The common ratio of a geometric sequence is -4 and the third term is 400. Find the sum of the third through the tenth term of the sequence.
Title: Jul 217:09 AM (12 of 20)
Infinite Series Look at 2(½)x-1 .
If the sequence of partial sums (all of which are true sums) approaches a finite limit S, then the Infinite Series CONVERGES.
If the limit of the partial sums does not exist, then the series diverges and has no sum.
Title: Jul 207:19 AM (13 of 20)
Let‛s look: a) 0.1, 0.01, 0.001, 0.0001, …
b) 10 + 20 + 30 + 40 + …
c) 1 - 1 + 1 - 1 + …
Title: Jul 207:20 AM (14 of 20)
Convergence of Geometric Series
sum:
converges iff |r| < 1. If it does converge, the sum is a/(1 - r)
Title: Jul 207:21 AM (15 of 20)
Does the series converge? If it does, what is its sum.
Title: Jul 207:22 AM (16 of 20)
1 + ½ + ¼ + 1/8 + …
Title: Jul 207:22 AM (17 of 20)
Find the sum of the following geometric series. 3 + 3/4 + 3/16 + 3/64 + ...
Title: Jul 217:07 AM (18 of 20)
Find the sum of the following geometric series. 5 - 5/2 + 5/4 - 5/8 - ...
Title: Jul 217:16 AM (19 of 20)
Title: Jul 2111:03 AM (20 of 20)
Title: Jul 206:54 AM (1 of 20)
The average of three successive terms of an arithmetic sequence is 47.2. What is the second of the three terms?
Title: Jul 216:58 AM (2 of 20)
The first term of an arithmetic sequence is 325, and the 82nd term is 352. Find the common difference and the sum of the 12th through the 82nd terms.
Title: Jul 216:59 AM (3 of 20)
The sum of two consecutive terms of an arithmetic sequence is 2. Their product is -24. The first of the two terms is smaller than the second. Find the two terms.
Title: Jul 217:00 AM (4 of 20)
The first term of an arithmetic series is 2 and the common difference is 3. The sum is 187. How many terms are in the series?
Title: Jul 217:12 AM (5 of 20)
The 452nd term of an arithmetic sequence is -893 and the 84th is 27. Find the first five terms of the sequence.
Title: Jul 217:05 AM (6 of 20)
Suppose that at the beginning of the year, your savings account contains $4250. If you withdraw $350 per month from the account, how much will it contain at the end of the year.
Title: Jul 217:06 AM (7 of 20)
The lengths of the sides of a right triangle form an arithmetic sequence with common difference 3. Find the lengths of the sides.
Title: Jul 217:14 AM (8 of 20)
Formula for Geometric Series
Title: Jul 207:12 AM (9 of 20)
Find the sum of the geometric sequence 4, -4/3, 4/9, -4/27, …, 4(-1/3) 10.
Title: Jul 207:19 AM (10 of 20)
Linda deposits $250 at the end of each month into an account that pays 3% interest compounded monthly. After 10 years, the balance in the account is
Find her balance.
Title: Jul 207:19 AM (11 of 20)
The common ratio of a geometric sequence is -4 and the third term is 400. Find the sum of the third through the tenth term of the sequence.
Title: Jul 217:09 AM (12 of 20)
Infinite Series Look at 2(½)x-1 .
If the sequence of partial sums (all of which are true sums) approaches a finite limit S, then the Infinite Series CONVERGES.
If the limit of the partial sums does not exist, then the series diverges and has no sum.
Title: Jul 207:19 AM (13 of 20)
Let‛s look: a) 0.1, 0.01, 0.001, 0.0001, …
b) 10 + 20 + 30 + 40 + …
c) 1 - 1 + 1 - 1 + …
Title: Jul 207:20 AM (14 of 20)
Convergence of Geometric Series
sum:
converges iff |r| < 1. If it does converge, the sum is a/(1 - r)
Title: Jul 207:21 AM (15 of 20)
Does the series converge? If it does, what is its sum.
Title: Jul 207:22 AM (16 of 20)
1 + ½ + ¼ + 1/8 + …
Title: Jul 207:22 AM (17 of 20)
Find the sum of the following geometric series. 3 + 3/4 + 3/16 + 3/64 + ...
Title: Jul 217:07 AM (18 of 20)
Find the sum of the following geometric series. 5 - 5/2 + 5/4 - 5/8 - ...
Title: Jul 217:16 AM (19 of 20)
Title: Jul 2111:03 AM (20 of 20)
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