Question

The average of 7 consecutive odd number is 33. What is the greatest number out of this

Answer 1

Let first number be x

So , The consecutive 7 numbers will be x , x + 1 , x + 2 , x + 3 , x + 4 , x +5 , x + 6

$\fbox{ \bold{ \: \: Average = \frac{Sum \: of \: all \: numbers \: }{Total \: numbers \: \: } </p><p> \: }}$

$\to \bold{ 33 =\frac{ \: x \: + x \: + \: 1+ \: x \: + \: 2 \: + \: x \: + \: 3 \: + \: x \: + \: 4 \: + \: x \: + \: 5 \: + \: x \: + \: 6 \: }{7} }\\ \\ \bold{\to 7x \: + \: 21=7 \times 33} \\ \\ \bold{ \to 7x \: = \: 231-21} \\ \\ \to </p><p> \bold{7x \: =210}</p><p> \\ \\ \bold{ \to x \: =30}$

$\therefore$ The largest number ( x + 6 ) is 30 + 6 i.e 36

Answer 2

Answer:

To know the odd numbers first we have to make an odd variable

if x is a number then (x*2) would always be an even number

and (x*2)+1 will be odd

So ,

let the first odd no. be (x*2)+1

next odd number will be (x*2)+3 .... and so on .

Average  = (x*2)+1 + (x*2)+3 + (x*2)+5 + (x*2)+7 + (x*2)+9 + (x*2)+11 + (x*2)+13/7

33 = 7(x*2) + 49/7

33 = 2x + 7

26 = 2x

x = 13

largest number is (x*2)+13

(x*2)+13 = 39  [ANSWER]