Lesson test: Sequences and series

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Sequences and series

1.[2p]
A sequence starts at 5 and rises by 3 each step. What is its thirtieth term?

CorrectNot quite: 92

2.[2p]
What is the sum of the first thirty terms of that sequence?

CorrectNot quite: 1455

3.[2p]
Sum the first ten terms of $3, 6, 12, 24, dots$

CorrectNot quite: 3069

4.[3p]
What is the sum of the infinite series $6 + 2.4 + 0.96 + dots$ ?

CorrectNot quite: 10

5.[3p]
An infinite geometric series converges exactly when

the common ratio satisfies $lvert r rvert < 1$

Correct

the terms shrink toward zero

The answer is: the common ratio satisfies $\lvert r \rvert < 1$

the first term is positive

The answer is: the common ratio satisfies $\lvert r \rvert < 1$

the common ratio is positive

The answer is: the common ratio satisfies $\lvert r \rvert < 1$

6.[2p]
The harmonic series $1 + 1 / 2 + 1 / 3 + dots$ converges, because its terms shrink to zero.

True

The answer is: False

False

Correct

7.[3p]
A mortgage of 200,000 pounds at a monthly rate of 0.0035 runs 300 months. What is the monthly payment, in pounds?

CorrectNot quite: 1077.88

8.[3p]
Euler's polynomial $n^{2} + n + 41$ gives a prime for $n = 0$ to $39$ and fails at $n = 40$ . What does that show?

Checking many cases is evidence, not proof

Correct

The polynomial was written down wrongly

The answer is: Checking many cases is evidence, not proof

Primes stop occurring above 1681

The answer is: Checking many cases is evidence, not proof

Counterexamples cannot exist for polynomial claims

The answer is: Checking many cases is evidence, not proof

9.[3p]
Match each sequence to what it is.

$7, 11, 15, 19$
$3, 6, 12, 24$
$1, 1, 2, 3, 5$
$1, 1 / 2, 1 / 3, 1 / 4$

recursive, each term the sum of the two before
harmonic, and its series diverges
arithmetic, difference 4
geometric, ratio 2

Show the answer

$7, 11, 15, 19$ : arithmetic, difference 4 $3, 6, 12, 24$ : geometric, ratio 2 $1, 1, 2, 3, 5$ : recursive, each term the sum of the two before $1, 1 / 2, 1 / 3, 1 / 4$ : harmonic, and its series diverges

1.[2p] A sequence starts at 5 and rises by 3 each step. What is its thirtieth term?

2.[2p] What is the sum of the first thirty terms of that sequence?

3.[2p] Sum the first ten terms of 3,6,12,24,dots

4.[3p] What is the sum of the infinite series 6+2.4+0.96+dots?

5.[3p] An infinite geometric series converges exactly when

6.[2p] The harmonic series 1+1/2+1/3+dots converges, because its terms shrink to zero.

7.[3p] A mortgage of 200,000 pounds at a monthly rate of 0.0035 runs 300 months. What is the monthly payment, in pounds?

8.[3p] Euler's polynomial n2+n+41 gives a prime for n=0 to 39 and fails at n=40. What does that show?

9.[3p] Match each sequence to what it is.

1.[2p]
A sequence starts at 5 and rises by 3 each step. What is its thirtieth term?

2.[2p]
What is the sum of the first thirty terms of that sequence?

3.[2p]
Sum the first ten terms of $3, 6, 12, 24, dots$

4.[3p]
What is the sum of the infinite series $6 + 2.4 + 0.96 + dots$ ?

5.[3p]
An infinite geometric series converges exactly when

6.[2p]
The harmonic series $1 + 1 / 2 + 1 / 3 + dots$ converges, because its terms shrink to zero.

7.[3p]
A mortgage of 200,000 pounds at a monthly rate of 0.0035 runs 300 months. What is the monthly payment, in pounds?

8.[3p]
Euler's polynomial $n^{2} + n + 41$ gives a prime for $n = 0$ to $39$ and fails at $n = 40$ . What does that show?

9.[3p]
Match each sequence to what it is.