Question

The 4th term of the AP is 3 times it's first term and the 7th term exceeds the 3rd term by 1. Find the 10th term ​

Answer 1

Answer:

let a1,a2,a3 ,.........,a7 are in a.p. whose common difference is d

a4 = 3a1

a1 + 3d = 3a1

3d = 2a1

a7 = 2a3 + 1

a1 + 6d = 2a1 + 4d + 1

2d = a1 + 1

4a1/3 = a1 + 1

a1 = 3

d = 2

a10= a +9d

= 3+9*2

3+18

=21

Step-by-step explanation:

Answer 2

Answer :-

• The 10th term is 21/8.

Given :-

• The 4th term of the AP is 3 times it's first term and the 7th term exceeds the 3rd term by 1.

To Find :-

• 10th term of the AP.

Solution :-

• 7th term of the AP = T7 (a + 6d)
• 3rd term of the AP = T3 (a + 2d)
• 10th term of the AP = T10 (a + 9d)
• 4th term of the AP = T4 (a + 3d)

7th term of the AP exceeds the 3rd term by 1

⇒T7 - T3 = 1

⇒ (a + 6d) - (a + 2d) = 1

⇒ a + 6d - a - 2d = 1

⇒ 6d - 2d = 1

⇒ 4d = 1

⇒ d = 1/4

Here

• T4 = 3a

Now

⇒ a + 3d = 3a

⇒ 3a - a = 3d

⇒ 2a = 3d

⇒ 2a = 3/4

⇒ a = 3/4/2

⇒ a = 3/8

We'll find 10th term

⇒T10 = a + 9d

⇒ T10 = 3/8 + 9(1/4)

⇒ T10 = 3/8 + 9/4

⇒ T10 = (3 + 18)/8

⇒ T10 = 21/8

Hence, the 10th term is 21/8.