Chapter 12: Q. 21 (page 838)

In Problems 20 and 21, find a general formula for each arithmetic sequence.
10th term is 0
18th term is 8

Short Answer

Expert verified

The general formula of the sequence is: $\{a_{n}\} = \{n - 10\}$

Step by step solution

Step 1. Given information

In an arithmetic sequence :

$a_{10} = 0 a_{18} = 8$

Let $a$ is the first term and $d$ is the common difference of the sequence.

Step 2. Make two equations of a and d

According to the given condition,

$a_{10} = 0 a + (10 - 1) d = 0$

a + 9 d = 0

.......... equation (1)

$a_{18} = 8 a + (18 - 1) d = 8$ .

$a + 17 d = 8$ ...............equation (2)

Step 3. Solve equations.

Substract equation (1) from (2)

$(a + 17 d) - (a + 9 d) = 8 - 0 8 d = 8 d = 1$

Substitute this value in the equation (1)

$a + 9.1 = 0 a + 9 = 0 a = - 9$

Step 4. General formula for sequence.

Substitute values of $a$ and $d$ in general formula of arithmetic sequence.

a_{n} = a + (n - 1) d = - 9 + (n - 1) . 1 = - 9 + n - 1 = n - 10

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In Problems 20 and 21, find a general formula for each arithmetic sequence.
10th term is 0
18th term is 8

Short Answer

Step by step solution

Step 1. Given information

Step 2. Make two equations of a and d

Step 3. Solve equations.

Step 4. General formula for sequence.

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In Problems 20 and 21, find a general formula for each arithmetic sequence.10th term is 018th term is 8

Short Answer

Step by step solution

Step 1. Given information

Step 2. Make two equations of a and d

Step 3. Solve equations.

Step 4. General formula for sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In Problems 20 and 21, find a general formula for each arithmetic sequence.
10th term is 0
18th term is 8