Question

The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the 5 term of an ap​

Answer 1

5th term of an A.P = 7

Step-by-step explanation:

Given :-

• The sum of 4th and 8th term of an A.P is 24.
• the sum of the 6th and 10th terms is 44 .

To find :-

• find the 5th term of an A.P

Solution :-

4th term of an A.P = a + 3d

8th term of an A.P = a + 7d

Sum of 4th term and 8th term = 24

a + 3d + a + 7d = 24

2a + 10d = 24

divided by 2

a + 5d = 12 ...........eq.(1)

6th term of an A.P = a + 5d

10th term of an A.P = a + 9d

Sum of 6th term and 10th term = 44

a + 5d + a + 9d = 44

2a + 14 = 44

divided by 2

a + 7d = 22 ..........eq.(2)

Subtract eq.(1) from eq.(2)

a + 7d = 22

a + 5d = 12

2d = 10

⟼ d = 10/2

⟼ d = 5

Put the value of d = 5 in eq.(1) we get :-

⟼ a + 5d = 12

⟼ a + 5 × 5 = 12

⟼ a + 25 = 12

⟼ a = 12 – 25

⟼ a = –13

Now, 5th term of an A.P = a + 4d

Put the value of a and d we get :-

⟼ a_5 = a + 4d

⟼ a_5 = –13 + 4 × 5

⟼ a_5 = –13 + 20

⟼ a_5 = 7

Hence, 5th term of an A.P = 7

Here,

• a = first term of an A.P
• d = common difference of an A.P