Step-by-step explanation:

Sure, here are the answers to your questions:

**a) What is the common difference?**

The common difference is the difference between any two consecutive terms in the sequence. In this case, the common difference is 8 - 5 = 3.

**b) What is the difference between its 10th and 18th terms?**

The 10th term in the sequence is 5 + 9 * 3 = 32. The 18th term in the sequence is 5 + 17 * 3 = 62. The difference between these two terms is 62 - 32 = 30.

**c) Is 100 a term of this sequence? Why?**

No, 100 is not a term of this sequence. The sequence increases by 3 each time, so it would take 100 / 3 = 33.33 terms to reach 100. Since the sequence only has 21 terms, 100 is not a term of the sequence.

**d) What is the 21st term of this sequence?**

The 21st term of the sequence is 5 + 20 * 3 = 65.

Here are the equations for the answers to your questions:

**a)** Common difference = 8 - 5 = 3

**b)** Difference between 10th and 18th terms = 62 - 32 = 30

**c)** 100 / 3 = 33.33, so 100 is not a term of the sequence

**d)** 21st term = 5 + 20 * 3 = 65

I hope this helps! Let me know if you have any other questions.

a) The common difference = 3

b) The difference between its 10th and 18th terms = 24

c) No, 100 is not a term in this sequence.

d) The 21st term of this series is 65.

Given:

An arithmetic sequence- 5, 8, 11,...

To Find:

a) The common difference =/

b) The difference between its 10th and 18th terms =?

c) Whether 100 is a term in this sequence or not.

d) The 21st term of this series =?

Solution:

When a series or sequence is increasing or decreasing by a constant term then that series is an arithmetic series.

The arithmetic series is given by a, a + d, a + 2d,...

Here, a is the first term.

a + d - a = a + 2d - a - d = d

d is the common difference.

The nth term of the series is given by

aₙ = a + (n - 1)d

The sequence given is

5, 8, 11,...

The first term, a = 5

a) The common difference = difference between any two consecutive terms.

The first term = 5

Second term = 8

The common difference = 8 - 5

The common difference, d = 3

b) 10th term = a + (10 - 1)d

10th term = a + 9d

18th term = a + (18 - 1)d

18th term = a + 17d

The difference between its 10th and 18th terms

= a + 17d - (a + 9d)

= a + 17d - a - 9d

= 8d

= 8 × 3

= 24

Therefore, the difference between its 10th and 18th terms = 24

c) Let the nth term of the sequence be 100.

100 = 5 + (n - 1)3

100 - 5 = (n - 1)3

(n - 1)3 = 95

n - 1 = 95/3

n - 1 = 31.67

n = 31.67 + 1

n = 32.67

Since the sequence is not in fractions, the nth term will also not be in fractions.

Therefore, 100 is not a term of this sequence.

d) n = 21

21st term = a + (21 - 1)d

21st term = a + 20d

21st term = 5 + 20 × 3

21st term = 5 + 60

21st term = 65

a) The common difference = 3

b) The difference between its 10th and 18th terms = 24

c) No, 100 is not a term in this sequence.

d) The 21st term of this series is 65.

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