## Arithmetic Sequence Problems Using Gauss’s Strategy### To determine#### (b)**To find:**The sum of the arithmetic sequence \[1 + 3 + 5 + 7 + \cdots + 1001\] using Gauss’s strategy.### To determine#### (c)**To find:**The sum of the arithmetic sequence \[3 + 6 + 9 + 12 + \cdots + 300\] using Gauss’s strategy.### To determine#### (d)**To find:**The sum of the arithmetic sequence \[4 + 8 + 12 + 16 + \cdots + 400\] using Gauss’s strategy.**Note:** Gauss’s strategy, often referred to in the context of summing arithmetic sequences, involves pairing numbers from the beginning and end of the sequence to simplify the summation process. For an arithmetic sequence, the key formula is:\[\text{Sum} = \frac{N}{2} \times (\text{First Term} + \text{Last Term})\]where $N$ is the number of terms in the sequence.

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Description: ## Arithmetic Sequence Problems Using Gauss’s Strategy### To determine#### (b)**To find:**The sum of the arithmetic sequence \[1 + 3 + 5 + 7 + \cdots + 1001\] using Gauss’s strategy.### To determine#### (c)**To find:**The sum of the arithmetic seque

Gauss took 2 numbers(smallest and largest) of a series at a time to make a pair and added them to…

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3:55 1 Try solving a math problem by scanning X it with your phone. (b) To find: The sum of the arithmetic sequence 1+3+5+7+... + 1001 using Gauss's strategy. To determine To find: The sum of the arithmetic sequence 3+ 6+9 + 12 + ... + 300 using Gauss's strategy. To determine (d) To find: The sum of the arithmetic sequence 4+8 + 12 + 16+ ... + 400 using Gauss's VX

3:55 1 Try solving a math problem by scanning X it with your phone. (b) To find: The sum of the arithmetic sequence 1+3+5+7+... + 1001 using Gauss's strategy. To determine To find: The sum of the arithmetic sequence 3+ 6+9 + 12 + ... + 300 using Gauss's strategy. To determine (d) To find: The sum of the arithmetic sequence 4+8 + 12 + 16+ ... + 400 using Gauss's VX

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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## Arithmetic Sequence Problems Using Gauss’s Strategy

### To determine

#### (b)
**To find:**
The sum of the arithmetic sequence
\[1 + 3 + 5 + 7 + \cdots + 1001\]
using Gauss’s strategy.

### To determine

#### (c)
**To find:**
The sum of the arithmetic sequence
\[3 + 6 + 9 + 12 + \cdots + 300\]
using Gauss’s strategy.

### To determine

#### (d)
**To find:**
The sum of the arithmetic sequence
\[4 + 8 + 12 + 16 + \cdots + 400\]
using Gauss’s strategy.

**Note:** Gauss’s strategy, often referred to in the context of summing arithmetic sequences, involves pairing numbers from the beginning and end of the sequence to simplify the summation process. For an arithmetic sequence, the key formula is:
\[
\text{Sum} = \frac{N}{2} \times (\text{First Term} + \text{Last Term})
\]
where $N$ is the number of terms in the sequence.

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