Question

The sum of 4 consecutive even numbers is 163 more than the sum of three consecutive odd numbers. if the sum of smallest odd number and the smallest even number is 69, what is the largest odd number ?

Answer 1

the largest odd number will be 21

Answer 2

The largest odd number will be 21

CONCEPT- Sum of numbers in arithmetic progression.

Arithmetic numbers- List of numbers where difference between any two consecutive number is same.

Here in both odd number and even number the difference would 2 so they are in arithmetic progression.

Sum of numbers in arithmetic progression are

$n/2 \: [2a+(n-1) \: d]$

Here

$n= no \: of \: terms$

$a= First \: term$

$d = difference \: btw \: consecutive \: no$

For 4 consecutive even nos it would be:

Let A be the first no

$4/2 \: [2A+(4-1)×2$

$= 2[2A+6]$

$= 4A+12$

Now For 3 consecutive odd nos

Let a be the first no

$3/2 \: [2a+(3-1)×2$

on solving it comes

$3a+6$

In the question it is given that the sum of even consecutive nos is 163 more than sum of odd consecutive nos so :-

$3a+6+163= 4A+12$

$= 4A-3a=157 \: \: \: ①$

Also it is given in question that sum of the smallest odd and the smallest even no is 69.

Smallest no is the first no in both cases ie A and a so:

$A+a= 69 \: \: \: \:$

Multiplying the above by 4 so

4A+4a= 276

$4A= 276-4a \: \: ②</p><p></p><p>$

putting the ② in ① we get

$276-4a-3a=157$

$7a=119$

$a=17$

So our smallest odd number (a) is 17

The largest odd number will be :

$17+2+2 = 21$

As there are only three consecutive odd numbers and the difference between each number is 2 .

Further links

https://www.google.com/url?sa=t&source=web&rct=j&url=https://brainly.in/question/3719232&ved=2ahUKEwjlnN7Wqtr5AhU62XMBHbvRD8wQjjh6BAgHEAE&usg=AOvVaw3-yFNtybdew9nJwqcbUyTj

https://brainly.in/question/47065448

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