if 9th term of an ap is zero prove that it 29th term is double its 19th term
Answers
Step-by-step explanation:
Given:
a9= 0
=> a+8d = 0
=> a = -8d
To prove:
a29 = 2 a19
LHS:
a29 = a+28d
substitute a=-8d
a29 = -8d + 28d = 20d
RHS:
a19 = a + 18d
substitute a=-8d
a19 = -8d + 18d = 10d
2 a19 = 2(10d) = 20d
LHS = RHS
Hence proved.
Hope it helps you:)
Answer:
Step-by-step explanation:
Given:
- The 9th term of an A.P is 0
To Prove:
- The 29th term of the A.P is double its 19th term
Proof:
By given the ninth term of the A.P is 0.
a₉ = 0
The nth term of an A.P is given by,
aₙ = a₁ + (n - 1) × d
where a₁ is the first term,
aₙ is the nth term
d is the common difference
Therefore,
a₉ = a₁ + 8d = 0
a₁ = -8d----(1)
Now the 29th term of the A.P is given by,
a₂₉ = a₁ + 28 d
Substitute the value of a₁ from equation 1,
a₂₉ = -8d + 28 d
a₂₉ = 20 d
a₂₉ = 2 × (10 d)
a₂₉/2 = 10 d----(2)
Now the 19th term of the A.P is given by,
a₁₉ = a₁ + 18 d
Substituting value of a₁ from equation 1,
a₁₉ = -8d + 18 d
a₁₉ = 10d----(3)
From equations 2 and 3, RHS are equal, therefore LHS must also be equal.
Hence,
a₁₉ = a₂₉/2
a₂₉ = 2 × a₁₉
That is the 29th term is double the 19th term.
Hence proved.