Chapter 12: Q 116 (page 1185)

Find the sum of the first 50 terms of the arithmetic sequence whose general term is given.
$a_{n} = - 4 n + 3$

Short Answer

Expert verified

The obtained sum is -4950.

Step by step solution

Step 1. Given Information.

The given general formula is $a_{n} = - 4 n + 3$ .

Step 2. Find the first and 50th terms.

Substitute 1 for n in the formula for the first term.

$\begin{array}{rcl} a_{1} & = & - 4 (1) + 3 \\ = & - 1 \end{array}$

Substitute 50 for n in the formula for the 50th term.

$\begin{array}{rcl} a_{50} & = & - 4 (50) + 3 \\ = & - 200 + 3 \\ = & - 197 \end{array}$

Step 3. Find the sum of 50th terms.

Use the formula of sum $S_{n} = \frac{n}{2} (a_{1} + a_{n})$ .

$\begin{array}{rcl} S_{50} & = & \frac{50}{2} (- 1 - 197) \\ = & 25 (- 198) \\ = & - 4950 \end{array}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find the sum of the first 50 terms of the arithmetic sequence whose general term is given.
$a_{n} = - 4 n + 3$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Find the first and 50th terms.

Step 3. Find the sum of 50th terms.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Decision Maths

Geometry

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the sum of the first 50 terms of the arithmetic sequence whose general term is given. an=−4n+3

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Find the first and 50th terms.

Step 3. Find the sum of 50th terms.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Decision Maths

Geometry

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the sum of the first 50 terms of the arithmetic sequence whose general term is given.
$a_{n} = - 4 n + 3$