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

Answer: (c)

Five consecutive integers are :

x, x + 1, x + 2, x + 3 and x + 4

∴ Their average

= ${x+x+1+x+2+x+3+x+4}/5$

= ${5x+10}/5$ = x+2

New average

= ${(5x+10)+x+5+x+6}/7$

= ${7x+21}/7$= x + 3

Difference = x + 3 – x – 2 = 1

Answer: (a)

Using Rule 4,

Average of $1^2,2^2,3^2,4^2…x^2$ = ${(n+1)(2n+1)}/6$

${1^2+2^2+3^2+…+n^2}/n$ = ${(n+1)(2n+1)}/6$

∴ ${1^2+2^2+3^2+…+10^2}/10$ = ${(10+1)(2×10+1)}/6$

= ${11×21}/6$ = 38.5

Answer: (c)

Formula,

Average of the first n natural odd numbers = $n/2$

Number of odd numbers upto $100/2$ = 50 = required average

Aliter : Using Rule 7,

Odd numbers are 1, 3, 5, ............., 99

Total odd numbers are= 50

∴ Average = 50

Answer: (a)

Let the first number be x.

∴ x + 3 + x + 4 = 2 × 6

⇒ 2x + 7 = 12

⇒ 2x = 5 ⇒ x =$5/2$

∴ x + (x + 1) + ....... + (x + 7) = 8x + 28

= 8×$5/2$+ 28 = 20 + 28 = 48

Answer: (b)

Required average

= ${3(1+2+3+…+9)}/9$

= ${9×10}/{2×3}$ = 15

Aliter : Using Rule 9,

Here, n = 9, x = 3

Average = x$({1+n}/2)$

= 3$({1+9}/2)$ = 15

Answer: (d)

Average of 25 consecutive odd numbers = 55

∴ Mid number i.e. 13th number = 55

∴ 25th number = 55 + 2 × 12

= 55 + 24 = 79