7th term of a HP is 3/2 and it's 10th term is 12/17 find its 8th term
Answers
Given
7th term of HP is 3/2
10th term of HP is 12/17
To Find
8th term of HP
We know That
HP = 1/AP
7th term of AP is 2/3
10th term of AP is 17/12
Formula
Tₙ = a + (n - 1)d
T₇ = a + (7 -1)d
a + 6d = 2/3 (i)eq
Now Take
T₁₀ = a + (10 -1)d
a+ 9d = 17/12 (ii)eq
We Have
a + 6d = 2/3 (i)eq
a+ 9d = 17/12 (ii)eq
Subtract (ii) from (i)
a + 6d - (a + 9d) = 2/3 -17/12
a + 6d - a - 9d = 8/12 - 17/12
-3d = -9/12
d = 3/12
d = 1/4
Put the value of d on (i) eq
a + 6d = 2/3 (i)
a + 6(1/4) = 2/3
a + 6/4 = 2/3
a + 3/2 = 2/3
a = 2/3 - 3/2
a = (4 - 9)/6
a = -5/6
Now 8th Term of AP
T₈ = a +(n-1)d
T₈ = -5/6 + 7×1/4
T₈ = -5/6 + 7/4
T₈ = (-10 + 21)/12
T₈ = 11/12
8th term of HP is 12/11
Step-by-step explanation:
8 answers
Given
7th term of HP is 3/2
10th term of HP is 12/17
To Find
8th term of HP
We know That
HP = 1/AP
7th term of AP is 2/3
10th term of AP is 17/12
Formula
Tₙ = a + (n - 1)d
T₇ = a + (7 -1)d
a + 6d = 2/3 (i)eq
Now Take
T₁₀ = a + (10 -1)d
a+ 9d = 17/12 (ii)eq
We Have
a + 6d = 2/3 (i)eq
a+ 9d = 17/12 (ii)eq
Subtract (ii) from (i)
a + 6d - (a + 9d) = 2/3 -17/12
a + 6d - a - 9d = 8/12 - 17/12
-3d = -9/12
d = 3/12
d = 1/4
Put the value of d on (i) eq
a + 6d = 2/3 (i)
a + 6(1/4) = 2/3
a + 6/4 = 2/3
a + 3/2 = 2/3
a = 2/3 - 3/2
a = (4 - 9)/6
a = -5/6
Now 8th Term of AP
T₈ = a +(n-1)d
T₈ = -5/6 + 7×1/4
T₈ = -5/6 + 7/4
T₈ = (-10 + 21)/12
T₈ = 11/12
8th term of HP is 12/11