Chapter 12: Q. 322 (page 1222)

Find a general term for the sequence, $- \frac{2}{3}, - \frac{4}{5}, - \frac{6}{7}, - \frac{8}{9}, - \frac{10}{11}, . . .$

Short Answer

Expert verified

The general form of the sequence $- \frac{2}{3}, - \frac{4}{5}, - \frac{6}{7}, - \frac{8}{9}, - \frac{10}{11}, . . .$ is $a_{n} = \frac{2 n}{2 n + 1}$

Step by step solution

Step 1. Given

The sequence $- \frac{2}{3}, - \frac{4}{5}, - \frac{6}{7}, - \frac{8}{9}, - \frac{10}{11}, . . .$

To find the general form of the sequence.

Step 2. Look for a pattern in the terms.

Let us look for a pattern in the terms.

$- \frac{2 (1)}{2 (1) + 1}, - \frac{2 (2)}{2 (2) + 1}, - \frac{2 (3)}{2 (3) + 1}, - \frac{2 (4)}{2 (4) + 1}, - \frac{2 (5)}{2 (5) + 1}, . . .$

Step 3. General form of the sequence

By observing the pattern, we can find that he numerator is twice the number of terms and the denominator is one more than the twice the number of terms.

So, the general form is $a_{n} = \frac{2 n}{2 n + 1}$

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Find a general term for the sequence, $- \frac{2}{3}, - \frac{4}{5}, - \frac{6}{7}, - \frac{8}{9}, - \frac{10}{11}, . . .$

Short Answer

Step by step solution

Step 1. Given

Step 2. Look for a pattern in the terms.

Step 3. General form of the sequence

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Short Answer

Step by step solution

Step 1. Given

Step 2. Look for a pattern in the terms.

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One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Study anywhere. Anytime. Across all devices.

Find a general term for the sequence, $- \frac{2}{3}, - \frac{4}{5}, - \frac{6}{7}, - \frac{8}{9}, - \frac{10}{11}, . . .$