If the 5th term of an A.P is 10 and the sum of 4th and 8th terms is 30,then find the
A.P.
Answers
Answer:
In an A.P., uₙ = a + (n - 1) d
u₄ + u₈ = 24 (given)
a +3d + a + 7d = 24
2a + 10d = 24
a + 5d = 12 …..eq(1)
u₆ + u₁₀ = 34 (given)
a + 5d + a + 9d = 34
2a + 14d = 34
a + 7d = 17 …..eq(2)
eq(2) -(1) ⇒ 2d = 5
d = 5/2
Substitute d = 5/2 in eq (1)
a + 5(5/2) = 12
a + 25/2 = 12
a = -1/2
first term = a = -1/2
common difference =d = 5/2
Step-by-step explanation:
If the sum of 4th and 8th terms of an A.P. is 24, and the sum of 6th and 10th terms is 34, what is the 1st term and the common difference?
Let a be the first term and d be the common difference of AP
a4+a8=24⟹(a+3d)+(a+7d)=24⟹2a+10d=24
⟹a+5d=12(1)
a6+a10=34⟹(a+5d)+(a+9d)=34⟹2a+14d=34
⟹a+7d=17(2)
by (2) - (1)
2d=5⟹d=52
a+5d=12⟹a+5×52=12⟹a+252=12
⟹a=12−252=−12
The 3rd term of an AP is thrice the 7th term. If its 8th term is -12, what is the sum of the first 30 terms?
The sum of the 6th and 8th term of an AP is 40 and the product of the 4th and 7th term is 220. What is the AP?
If the 4th term of an AP is -7 and 7th term is -7 and 7th term is -22 find the sum of its first 24 terms?
What is the sum of 21 terms of A.P. -30, -27, and -24?
The 4th term of an A.P. is twice the 8th term. If its 6th term is -8, what is the sum of the first 200 terms?
In an A.P., uₙ = a + (n - 1) d
u₄ + u₈ = 24 (given)
a +3d + a + 7d = 24
2a + 10d = 24
a + 5d = 12 …..eq(1)
u₆ + u₁₀ = 34 (given)
a + 5d + a + 9d = 34
2a + 14d = 34
a + 7d = 17 …..eq(2)
eq(2) -(1) ⇒ 2d = 5
d = 5/2
Substitute d = 5/2 in eq (1)
a + 5(5/2) = 12
a + 25/2 = 12
a = -1/2
first term = a = -1/2
common difference =d = 5/2