model 2 average of consecutive numbers Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

Let three consecutive even numbers be x, x + 2 and x + 4. According to the question,

(x + x + 2 + x + 4) – ${x+x+2+x+4}/3$= 28

⇒ (3x + 6) – ${3x+6}/3$ = 28

⇒ (3x + 6) – (x + 2) = 28

⇒ 3x + 6 – x – 2 = 28

⇒ 2x + 4 = 28

⇒ 2x = 28 – 4 = 24

⇒ x = $24/2$ = 12

Answer: (a)

Using Rule 1,

Average of numbers = ${x_1+x_2+…+x_n}/n$

The required average

=${2+3+5+7+11+13+17+19+23}/9$

=$100/9$ = 11 $1/9$

Answer: (d)

Average of 25 consecutive odd numbers = 55

∴ Mid number i.e. 13th number = 55

∴ 25th number = 55 + 2 × 12

= 55 + 24 = 79

Answer: (b)

If the smallest number be x, then

$x/3$+12 = x+2

⇒ x + 36 = 3x + 6

⇒ 3x – x = 36 – 6

⇒ 2x = 30 ⇒ x = 15

∴ Third number = 15 + 4 = 19

Answer: (c)

Average of 7 consecutive numbers is 20.

Since the numbers are consecutive, they form an arithmetic series with common difference 1.

Since, 7 is odd, 20 must be the middle number.

We can write the series as below,

17, 18, 19, 20, 21, 22, 23

∴ The largest of these numbers is 23.

Answer: (d)

m + m + 1 + m + 2 + m + 3 + m + 4 = 5n

⇒ 5m + 10 = 5n

⇒ m + 2 = n ....(i)

Required average = ${m+2+m+3+m+4+m+5+m+6+m+7}/6$

= ${6m+27}/6$

= ${2m+9}/2$ = ${2(n-2)+9}/2$= ${2n+5}/2$ By (i) [m = n – 2]