Question

Divide 25 into 5 parts in A.P. such that the first and the last term are in the ratio 2:3. Then what will be it's 10th term?

Answer 1

AnswEr :

• Divide 25 into 5 parts in A.P. such that First term and Last Term are in Ratio 2:3
• Find the 10th Term of A.P.

Let the Terms be (a - 2d), (a - d) , a, (a + d), (a + 2d) where d is the difference.

• According to Question Now :

⇒ (a - 2d) + (a - d) + a + (a + d) + (a + 2d) = 25

⇒ a + a + a + a + a = 25

⇒ 5a = 25

• Dividing Both term by 5

⇒ a = 5

• Again According to Question :

⇒ 1st Term : 5th Term = 2 : 3

⇒ (a - 2d) / (a + 2d) = 2 / 3

• By Cross Multiplication

⇒ 3 × (a - 2d) = 2 × (a + 2d)

⇒ 3a - 6d = 2a + 4d

⇒ 3a - 2a = 4d + 6d

⇒ a = 10d

• Putting the Value of a = 5

⇒ 5 = 10d

• Dividing Both term by 5

⇒ 1 = 2d

⇒ d = 1 /2

⇒ d = 0.5

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➟ 10th Term of AP

➟ a + (n - 1)d

• Plugging the Values

➟ 5 + (10 - 1) × 0.5

➟ 5 + 9 × 0.5

➟ 5 + 4.5

➟ 9.5

჻ Hence, 10th Term of A.P. will be 9.5

Answer 2

Answer:

8.5

Step-by-step explanation:

(a-2d) +(a-d) +a+(a+d) +(a+2d)=25

5a-2d-d+d+2d=25

5a=25

a=5.

First term is a-2d

Last term is a+2d

Their ratio is 2:3

(a-2d) / (a+2d) =2/3

3a - 6d = 2a + 4d

-6d - 4d = +2a - 3a

-10d = - a

(a = 5)

-10/-5 =d

d= 0.5.

FIND THE 10th Term

The tenth term will be a + 7d

Because

a + 2d = 5th term

a + 3d = 6th term

a + 4d = 7th term

a + 5d = 8th term

a + 6d = 9th term

a + 7d = 10th term...

So,

For 10th term

a=5, d=0.5

a +7d = (5) + 7(0.5) = 8.5