Chapter 12: Q. 20 (page 816)

Find the $n$ th term of the arithmetic sequence $\{a_{n}\}$ whose initial term $a_{1}$ and common difference $d$ are given. What is the fifty-first term?
$a_{1} = 1; d = - \frac{1}{3}$

Short Answer

Expert verified

The $n$ th term is localid="1648724949517" $a_{n} = \frac{4}{3} - \frac{1}{3} n$ and the fifty-first term is $- \frac{47}{3}$ .

Step by step solution

Step 1. Given information

$a_{1} = 1; d = - \frac{1}{3}$

Step 2. Calculation

The $n$ th term is -

$a_{n} = a_{1} + (n - 1) d$

localid="1648724818307" $= 1 + (n - 1) (- \frac{1}{3})$

$= 1 - \frac{1}{3} n + \frac{1}{3}$

$= \frac{4}{3} - \frac{1}{3} n$

and the fifty-first term is -

localid="1648663826099" $a_{51} = 1 + (51 - 1) (- \frac{1}{3})$

localid="1648663834154" $= 1 + (50) (- \frac{1}{3})$

$= 1 + (- \frac{50}{3})$

$= - \frac{47}{3}$

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Find the $n$ th term of the arithmetic sequence $\{a_{n}\}$ whose initial term $a_{1}$ and common difference $d$ are given. What is the fifty-first term?
$a_{1} = 1; d = - \frac{1}{3}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Find the nth term of the arithmetic sequence anwhose initial term a1and common difference dare given. What is the fifty-first term?a1=1;d=-13

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Find the $n$ th term of the arithmetic sequence $\{a_{n}\}$ whose initial term $a_{1}$ and common difference $d$ are given. What is the fifty-first term?
$a_{1} = 1; d = - \frac{1}{3}$