which term of the ap 27,24,21,....... is zero
Answers
Answer:
The 10ᵗʰ term of the AP is 0.
Step-by-step-explanation:
The given arithmetic progression is 27, 24, 21, .....
We have to find which term of the progression is 0.
Now, the AP is 27, 24, 21, ....
t₁ = a = 27
t₂ = 24
t₃ = 21
Now,
d = t₂ - t₁
⇒ d = 24 - 27
⇒ d = - 3
∴ a = 27, d = - 3 & tₙ = 0
Now, we know that,
tₙ = a + ( n - 1 ) * d - - [ Formula ]
⇒ 0 = 27 + ( n - 1 ) * ( - 3 )
⇒ 0 = 27 - 3n + 3
⇒ 0 - 3n = 27 + 3
⇒ 3n = 30
⇒ n = 30 ÷ 3
⇒ n = 10
∴ The 10ᵗʰ term of the AP is 0.
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Additional Information:
1. Arithmetic Progression:
In a sequence, if the common difference between two consecutive terms is constant, then the sequence is called as Arithmetic Progression ( AP ).
2. nᵗʰ term of an AP:
The number of a term in the given AP is called as nᵗʰ term of an AP.
3. Formula for nᵗʰ term of an AP:
- tₙ = a + ( n - 1 ) * d
4. The sum of the first n terms of an AP:
The addition of either all the terms or a particular terms is called as sum of first n terms of an AP.
5. Formula for sum of the first n terms of an AP:
- Sₙ = n / 2 [ 2a + ( n - 1 ) * d ]
Answer:
The 10ᵗʰ term of the AP is 0.
Step-by-step-explanation:
The given arithmetic progression is 27, 24, 21, .....
We have to find which term of the progression is 0.
Now, the AP is 27, 24, 21, ....
t₁ = a = 27
t₂ = 24
t₃ = 21
Now,
d = t₂ - t₁
⇒ d = 24 - 27
⇒ d = - 3
∴ a = 27, d = - 3 & tₙ = 0
Now, we know that,
tₙ = a + ( n - 1 ) * d - - [ Formula ]
⇒ 0 = 27 + ( n - 1 ) * ( - 3 )
⇒ 0 = 27 - 3n + 3
⇒ 0 - 3n = 27 + 3
⇒ 3n = 30
⇒ n = 30 ÷ 3
⇒ n = 10
∴ The 10ᵗʰ term of the AP is 0.
─────────────────────
Additional Information:
1. Arithmetic Progression:
In a sequence, if the common difference between two consecutive terms is constant, then the sequence is called as Arithmetic Progression ( AP ).
2. nᵗʰ term of an AP:
The number of a term in the given AP is called as nᵗʰ term of an AP.
3. Formula for nᵗʰ term of an AP:
tₙ = a + ( n - 1 ) * d
4. The sum of the first n terms of an AP:
The addition of either all the terms or a particular terms is called as sum of first n terms of an AP.
5. Formula for sum of the first n terms of an AP:
Sₙ = n / 2 [ 2a + ( n - 1 ) * d ]