How many even numbers are there between 31 and 1927?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Question:**
How many even numbers are there between 31 and 1927?
To find the number of even numbers between 31 and 1927, we need to identify the smallest and largest even numbers in this range.
The smallest even number greater than 31 is 32. The largest even number less than or equal to 1927 is 1926.
The sequence of even numbers between 32 and 1926 can be represented as:
32, 34, 36, ..., 1926.
This is an arithmetic sequence where the first term (a) is 32, the last term (l) is 1926, and the common difference (d) is 2.
The formula for the nth term of an arithmetic sequence is given by:
\[ a_n = a + (n-1)d \]
We need to find the number of terms (n). Solving for n:
\[ 1926 = 32 + (n-1) \times 2 \]
\[ 1926 = 32 + 2n - 2 \]
\[ 1926 = 30 + 2n \]
\[ 1896 = 2n \]
\[ n = 948 \]
So, there are 948 even numbers between 31 and 1927.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5f558a7-14fc-4024-84d6-4debb1adc6f6%2F4861a8eb-b0b1-41a4-b672-1cc579d072e1%2F3gzlkt6_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
How many even numbers are there between 31 and 1927?
To find the number of even numbers between 31 and 1927, we need to identify the smallest and largest even numbers in this range.
The smallest even number greater than 31 is 32. The largest even number less than or equal to 1927 is 1926.
The sequence of even numbers between 32 and 1926 can be represented as:
32, 34, 36, ..., 1926.
This is an arithmetic sequence where the first term (a) is 32, the last term (l) is 1926, and the common difference (d) is 2.
The formula for the nth term of an arithmetic sequence is given by:
\[ a_n = a + (n-1)d \]
We need to find the number of terms (n). Solving for n:
\[ 1926 = 32 + (n-1) \times 2 \]
\[ 1926 = 32 + 2n - 2 \]
\[ 1926 = 30 + 2n \]
\[ 1896 = 2n \]
\[ n = 948 \]
So, there are 948 even numbers between 31 and 1927.
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