The sum of 4th and 8th term of an ap is 24 and the sum of the 6th and 10th term is 34 find the first term and the common difference of the AP.
Answers
Answer:
a = -1/2
d = 5/2
Step-by-step explanation:
In AP, nth term = a + ( n - 1 )d, where a is first term and d is common difference.
Let the first term of this AP be a and common difference be d.
= > 4th term + 8th term = 24
= > a + 3d + a + 7d = 24
= > 2a + 10d = 24
= > 2( a + 5d ) = 24
= > a + 5d = 12
= > a = 12 - 5d ... (1)
Whereas,
= > 6th term + 10th term = 34
= > a + 5d + a + 9d = 34
= > 2a + 14d = 34
= > 2( a + 7d ) = 34
= > a + 7d = 17
= > 12 - 5d + 7d = 17 ... {from (1) }
= > 2d = 17 - 12
= > 2d = 5
= > d = 5/2
Hence,
= > a = 12 - 5d
= > a = 12 - 5(5/2)
= > a = (24-25)/2 = -1/2
Answer:
First term is -1/2 and common difference is 5/2.
Step-by-step explanation:
The sum of 4th and 8th term of an AP is 24.
→ a + (4-1)d + a + (8-1)d = 24
→ a + 3d + a + 7d = 24
→ 2a + 10d = 24
→ 2( a + 5d ) = 24
→ a + 5d = 12
→ a = 12 - 5d
Sum of the 6th and 10th term is 34.
→ a + (6-1)d + a + (10-1)d = 34
→ a + 5d + a + 9d = 34
→ 2a + 14d = 34
On taking 2 as common we get,
→ a + 7d = 17
→ a = 17 - 7d
On comparing both equations we get,
→ 12 - 5d = 17 - 7d
→ 12 - 17 = -7d + 5d
→ 5 = 2d
→ d = 5/2
So,
→ a = 12 - 5d
→ a = 12 - 5 × (5/2)
→ a = 12 - 25/2
→ a = (24 - 25)/2
→ a = -1/2