Question

Q.10) What is the sum of averages of first 30 natural numbers and first 20 natural numbers ?
explain STEP BY STEP​

Answer 1

$\boxed{\bf{\red{\longrightarrow Answer}}}$

• Sum of first 30 natural numbers:
• = 15(2+29)
• = 15(31)
• = 465
• Sum of first 20 natural numbers
• = 10(2+19)
• = 10(21)
• = 210

$\implies\texttt(\frac {465}{30})$

= 15.5

$\implies\texttt(\frac {</u><u>2</u><u>1</u><u>0</u><u>}{</u><u>2</u><u>0})$

= 10.5

• Sum of Averages = 10.5+15.5
• = 26

Answer 2

${\huge{\underline{\sf {\pink{Answer}}}}}$

$\boxed{ 26 }$

${\huge{\underline{\sf {\pink{Explanation :}}}}}$

First 30 natural numbers = 1, 2, 3, 4, ....... ,30

$\: \:$

The series is in an AP with,

First term (a) = 1

Last term (l) = 30

Common Difference (d) = 1

$\: \:$

$sum \: ({s}_{n}) = \frac{n}{2} (a + l)$

${s}_{30} = \frac{30}{2} (1 + 30)$

$\: \: \: \: \: \: \: = 15 \: \times \: (31)$

$\: \: \: \: \: \: \: = 465$

$\: \: \: \:$

$average \: = \: \frac{sum \: of \: observations}{no. \: of \: observations}$

$\: \: \: \: \: \: = \frac{465}{30}$

$\: \: \: \: \: \: = 15.5$

$\: \: \: \:$

Again,

First 20 natural numbers = 1, 2, 3, 4, ....... , 20

$\: \:$

The series is in an AP with,

First term (a) = 1

Last term (l) = 20

Common Difference (d) = 1

${s}_{20} = \frac{20}{2} (1 + 20)$

$\: \: \: \: \: \: \: \: = 10 \: \times \: (21)$

$\: \: \: \: \: \: \: \: \: = 210$

$\: \: \:$

$average \: = \: \frac{sum \: of \: observations}{no. \: of \: observations}$

$\: \: \: \: \: \: \: \: \: = \frac{210}{20}$

$\: \: \: \: \: \: \: = 10.5$

$\: \: \:$

Sum of average of first 30 natural numbers and first 20 natural numbers

= (15.5 + 10.5)

= 26