Question

Answeer it do ....
________​

Answer 1

$\red{ \bigstar}$ Information given to us:

• 30 students stands in the first row
• 27 students stands in second row
• 24 students stands in third row
• 6 students in last row

$\red{ \bigstar}$ What we have to calculate:

• Number of rows and total number of students?

$\red{ \bigstar}$Finding out common difference:

• $\implies$ 27 - 30 = -3
• $\implies$ 24 - 27 = -3

Therefore, common difference is -3

Calculations for number of rows:-

$\pink{ \bigstar}$Using Formula,

• l = a + (n - 1) d

It's an A.P. where,

• a is first term
• l is last term
• d is common difference
• n is number of terms

$\pink{ \bigstar}$Again we have,

• First term (a) is 30
• Common difference (d) is -3

We don't know about number of terms (n)

Let us find out!

$\pink{ \bigstar}$Substituting the values:

• ➳30 + (n - 1)-3 = 6
• ➳ 30 + (n - 1) × -3 = 6
• ➳30 - 3n + 3 = 6
• ➳ 30 - 3n = 6 - 3
• ➳ 30 - 3n = 3
• ➳ -3n = 3 - 30
• ➳ -3n = -27
• ➳ -n = -9
• ➳ n = 9

Thus, there are 9 rows.

Total number of students:-

$\blue{ \bigstar}$Using Formula,

Sum of n terms of an A.P.:

• $\dag \underline{\boxed{\sf{S \: = \: \dfrac{n}{2} \: [2a \: + \: (n \: - \: 1)d] }}}$

Where,

• a is first term
• d is common difference
• n is number of terms

$\blue{ \bigstar}$Again we have,

• Number of terms (n) is 9
• Common difference (d) is -3

$\blue{ \bigstar}$Substituting the values in the formula:

$: \leadsto \: \dfrac{9}{2} \times (2 \times 30 + 8 \times - 3)$

$: \leadsto \: \dfrac{9}{2} \times (60 - 24)$

$: \leadsto \: \dfrac{9}{2} \times 36$

$: \leadsto \: \dfrac{9}{ \cancel2} \times \cancel36$

$: \leadsto \: 9 \times 18$

$: \leadsto \: \boxed{162}$

Hence,

• Number of rows are 9 and total number of students are 162

More information:

• Arithmetic progression (A.P.) is a sequence in which each term can be found by adding a certain quantity to its preceding term
• Difference between two consecutive terms is called common difference
• Progression means it's a type of sequence in which each term is related to its predecessor and successor.

Answer 2

Given :-

→ Students stand in first row = 30.

→ Students stand in second row = 27.

→ Students stand in third row = 20.

→ Students stand in last row = 6.

▶To find :-

→ The total number of students.

▶ Solution :-

To obtain the total number of students, we have to add the numbers of students stands in each row .

So, Total number of students = Students stand in first row + Students stand in second row + Students stand in third row + Students stand in last row .

= 30 + 27 + 20 + 6 .

= 83.