Question

Q20. The average of 13 consecutive natural numbers in x. If the seventh number is 22, find x. A. 20 B. 22 C.28 D. 14​

Answer 1

The value of x us 22.

Step-by-step explanation:

As 22 is the 7th number, there are 6 numbers before it.

Let a be the first number.

22-6 = a = 16

So, add the numbers from 16 to 28 (16+12) and find average.

Answer 2

Answer:

If x is the average of 13 consecutive natural numbers and the seventh number is 22, then x is 22

Step-by-step explanation:

Given,

average of 13 consecutive natural numbers = x

Seventh number = 22

The 13 consecutive numbers are in AP

where 7 th term is 22 and the common difference is 1 ( as they are consecutive numbers)

So nth term in AP = a + ( n-1)d

Here n = 7

nth term = 22

And d = 1

So first term a is :

nth term - (n-1)d

= 22-[(7-1)*1]

= 22-6

= 16

So the 13 numbers are :

16,17,18,19,20,21,22,23,24,25,26,27,28

So average = sum of 13 numbers / 13

Sum of 13 numbers = Sum of 13 terms of the AP

That is,

$\frac{n}{2} (2a+(n-1)d)\\\\\frac{13}{2} (2*16+(13-1)*1)\\\\= \frac{13}{2} [32+12]\\\\= \frac{13}{2} *44\\\\=13*22\\\\=286$

So average = 286 /13

That is, x = 286/13

x = 22