$$T_{100} = 2 + (100-1) \times 3 = 299$$

$$T_5 = 3$$ \times $$2^{4} = 48$

Question 1

Given the arithmetic sequence $$2, 5, 8, \ldots$$, what is the 100th term of the sequence?

Accepted Answer

$$T_{100} = 2 + (100-1) 	imes 3 = 299$$

Question 2

Which formula correctly gives the sum of the first $$n$$ terms of an arithmetic series with first term $$a$$ and common difference $$d$$?

Accepted Answer

$$S_n = \dfrac{n}{2} [2a + (n-1)d]$$

Question 3

A geometric sequence has $$a = 3$$ and $$r = 2. $$What is the 5th term?

Accepted Answer

$$T_5 = 3$$ 	imes $$2^{4} = 48$

Question 4

Which of the following is the correct formula for the sum of the first $$n$$ terms of a geometric series with first term $$a$$ and ratio $$r 
eq 1$$?

Accepted Answer

$$S_n = a \dfrac{1 - r^n}{1 - r}$$

Question 5

If the sum of the first 20 terms of an arithmetic sequence is 710, and the first term is 5, what is the common difference?

Accepted Answer

$$d = 3$$

Question 6

A geometric series converges if and only if:

Accepted Answer

$$|r| \u003c 1$$

Question 7

Given the sigma notation $$\sum_{k=1}^{10} (2k-1)$$, what is the value of the sum?

Accepted Answer

$$100$$

Question 8

Which of the following sequences is an arithmetic sequence?

Accepted Answer

$$5, 8, 11, 14, \ldots$$

Question 9

If $$S_n = 2^n - 1 is $$the sum of the first $$n$$ terms of a sequence, what is the $$nth $$term $$T_n$$?

Accepted Answer

$$T_n = 2$$^{n}$$ - 2$$^{n-1}$$

Question 10

A staircase has 5 steps. Each step is 1 m wide and 0.2 m high. What is the total area of the vertical faces to be painted?

Accepted Answer

$$1 	ext{ m}^2$$

Question 11

Given the geometric sequence $$3, 6, 12, \ldots$$, what is the sum of the first 6 terms?

Accepted Answer

$$189$$

Question 12

If the sum of an infinite geometric series is $$S = \dfrac{a}{1-r}$$, what must be true about $$r$$?

Accepted Answer

$$|r| \u003c 1$$

Question 13

Which of the following is the general term for the arithmetic sequence with $$a = 7$$ and $$d = 4$$?

Accepted Answer

$$T_n = 7 + (n-1) 	imes 4$$

Question 14

If $$\sum_{k=1}^{n} k = 55$$, what is the value of $$n$$?

Accepted Answer

$$n = 10$$

Question 15

A geometric sequence has $$a = 5$$ and $$r = 0.5. $$What is the sum to infinity?

Accepted Answer

$$S_{\infty} = \dfrac{5}{1-0.5} = 10$$

Question 16

Which of the following sigma notations represents the sum of the first $$n$$ odd numbers?

Accepted Answer

$$\sum_{k=1}^{n} (2k-1)$$

Question 17

If the sum of the first $$n$$ terms of an arithmetic sequence is $$S_n = n^2$ + n$$, what is the common difference?

Accepted Answer

$$d = 2$$

Question 18

Given the sequence $$-3, -8, -13, \ldots$$, what is the sum of the first 20 terms?

Accepted Answer

$$S_{20} = -3 + (-8) + \ldots + T_{20} = -1,150$$

Question 19

If $$\sum_{k=1}^{n} 3^k = 363$$, what is the value of $$n$$?

Accepted Answer

$$n = 5$$

Sequences and Series: Arithmetic and Geometric Progressions

스터디 가이드 - 연습 문제