Chapter 12: Q 12.37. (page 1182)

Find the sum of the first 50 terms of the arithmetic sequence whose general term is $a_{n} = 2 n - 5$ .

Short Answer

Expert verified

The obtained sum is 2300.

Step by step solution

Step 1. Given Information.

The given general formula is $a_{n} = 2 n - 5$ .

Step 2. Find the first and 50th terms.

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

$\begin{array}{rcl} a_{1} & = & 2 (1) - 5 \\ = & - 3 \end{array}$

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

$\begin{array}{rcl} a_{50} & = & 2 (50) - 5 \\ = & 100 - 5 \\ = & 95 \end{array}$

Step 3. Find the sum of 50th terms.

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

$\begin{array}{rcl} S_{50} & = & \frac{50}{2} (- 3 + 95) \\ = & 25 (92) \\ = & 2300 \end{array}$

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Find the sum of the first 50 terms of the arithmetic sequence whose general term is $a_{n} = 2 n - 5$ .

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.

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Find the sum of the first 50 terms of the arithmetic sequence whose general term isan=2n-5.

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

Theoretical and Mathematical Physics

Statistics

Calculus

Geometry

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the sum of the first 50 terms of the arithmetic sequence whose general term is $a_{n} = 2 n - 5$ .