Chapter 12: Q. 27 (page 816)

Find the indicated term in each arithmetic sequence.
$80 th term of 2, \frac{5}{2}, 3, \frac{7}{2}, \dots$

Short Answer

Expert verified

The 80th term of the sequence is $\frac{83}{2} .$

Step by step solution

Step 1. Given information

$Thegivensequenceis 2, \frac{5}{2}, 3, \frac{7}{2}, \dots$

We have to find the 80th term of the sequence.

Step 2. Calculating the common difference.

$\begin{array}{l} \Rightarrow a_{1} = 2, a_{2} = \frac{5}{2}, a_{3} = 3, a_{4} = \frac{7}{2} \\ \Rightarrow a_{2} - a_{1} = \frac{5}{2} - 2 \\ = \frac{5 - 4}{2} \\ = \frac{1}{2} \\ \Rightarrow a_{3} - a_{2} = 3 - \frac{5}{2} \\ = \frac{6 - 5}{2} \\ = \frac{1}{2} \\ \Rightarrow commondifference, d = \frac{1}{2} \end{array}$

Step 3. Calculating the required term.

$\begin{array}{l} The n^{t h} termofasequenceisgivenas \\ a_{n} = a_{1} + (n - 1) d \\ Here, \\ a isthefirsttermofthesequence. \\ d isthecommondifference. \\ Thus, \\ \Rightarrow a_{80} = 2 + (80 - 1) (\frac{1}{2}) \\ = 2 + 79 \cdot (\frac{1}{2}) \\ = 2 + \frac{79}{2} \\ = \frac{2 \cdot 2 + 79}{2} \\ = \frac{4 + 79}{2} \\ = \frac{83}{2} \end{array}$

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Find the indicated term in each arithmetic sequence.
$80 th term of 2, \frac{5}{2}, 3, \frac{7}{2}, \dots$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the common difference.

Step 3. Calculating the required term.

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Find the indicated term in each arithmetic sequence.80th term of2,52,3,72,…

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the common difference.

Step 3. Calculating the required term.

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 the indicated term in each arithmetic sequence.
$80 th term of 2, \frac{5}{2}, 3, \frac{7}{2}, \dots$