model 4 find nth average from 1st & last number Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

Using Rule 1,

The sixth number

= 9 × 50 – 5 × 54 – 3 × 52

= 450 – 270 – 156 = 24

Answer: (c)

Using Rule 1,

Sum of 8 numbers = 20 × 8 = 160

Sum of the first two numbers =$31/2$ ×2 = 31

Sum of next three numbers = $64/3$×3=64

Sum of the remaining three numbers = 160 – (31 + 64) = 160 – 95 = 65

Let 6th number = x

∴ 7th number = x + 4,

8th number = x + 7

⇒ x + x + 4 + x + 7 = 65

⇒ 3x = 65 – 11

⇒ x = $54/3$ =18

∴ Eighth number = 18 + 7 = 25

Answer: (a)

Using Rule 1,

According to the question,

195 + x + x + 20 = 135 × 3

⇒ 2x + 215 = 405

⇒ 2x = 405 – 215 = 190

∴ x =$190/2$ = 95

x = Smallest number

Answer: (d)

Using Rule 1,

Average of two or more numbers/quantities is called the mean of these numbers, which is given by

$\text"Average(A)" = \text"Sum of observation / quantities"/\text"No of observation / quantities"$

∴ S = A × n

Sixth number

= 6 × 60 + 6 × 65 – 11 × 63

= 360 + 390 – 693 = 57

Answer: (b)

Using Rule 1,

Average of two or more numbers/quantities is called the mean of these numbers, which is given by

$\text"Average(A)" = \text"Sum of observation / quantities"/\text"No of observation / quantities"$

∴ S = A × n

Sixth result

= 6 × 49 + 6 × 52 – 11 × 50

= 294 + 312 – 550 = 56

Answer: (c)

Average of five numbers

= ${2×8+3×3}/{2+3}$

= ${16+ 9}/5$ = $25/5$ = 5