Question

the sum of 5th and 9th term of ap is 30 if its 8th term is 3 times its 25th term find ap

please answer fast​

Answer 1

Solution:

Given sum of 5th term and 9th term of AP=30

a+4d + a+8d =30

2a + 12 d = 30 ---equation (1)

Given that 25 term is three times of 3rd term in AP

25th term= 3 (8th term)

( a+ 24d)= 3(a +7d)

a+ 24d = 3a+ 21d

24d - 21 d= 3a- a

3d = 2a --- equation 2

Substitute the value of 2d in equation (1) we get

2a+ 12d = 30

3d +12d =30

15d =30

d = 2

2a = 3d

2a= 3x 2

2a= 6

a=3

THEREFORE AP is 3, 5,7, 9......

Answer 2

Width of rectangle is 25 cm.

Step-by-step explanation:

Given :-

A wire bend in form of square of side 30 cm.

Then wire is again bend in form of rectangle of length 35 cm.

To find :-

Width of the rectangle.

Solution :-

Here, Concept is : If we are bending wire in form of square than again bending it in rectangle. Than, perimeter of square will equal to perimeter of rectangle because we are not increasing length of wire by one measure we are bending it in square and rectangular shape.

So,

Perimeter of square = 4 × side

⟶ Perimeter = 4 × 30

⟶ Perimeter = 120

Thus,

Perimeter of square is 120 cm.

According to concept, Perimeter of square and perimeter of rectangle are equal.

So, Perimeter of rectangle is 120 cm.

Let, Breadth or width or rectangle be x cm.

We know,

Perimeter of rectangle = 2(Length + Breadth)

⟶ 120 = 2×(35 + x)

⟶ 120 = 70 + 2x

\⟶ 120 - 70 = 2x

⟶ 50 = 2x

⟶ 50/2 = x

⟶ x = 25

We take, Width of rectangle be x.

Therefore,

Width of rectangle is 25 cm.