the value of p for which (2p+1),10 and (5p+5) are three consecutive terms of an A.P is
Answers
Answer:
The value of p is 2.
Step-by-step-explanation:
We have given that,
( 2p + 1 ), 10 & ( 5p + 5 ) are three consecutive terms of an A.P.
Here,
- a = t₁ = ( 2p + 1 )
- t₂ = 10
- t₃ = ( 5p + 5 )
We know that,
The difference between two consecutive terms of an A.P., common difference ( d ) is constant.
∴ t₂ - t₁ = d - - ( 1 )
Also,
t₃ - t₂ = d - - ( 2 )
∴ t₂ - t₁ = t₃ - t₂ - - [ From ( 1 ) & ( 2 ) ]
⇒ 10 - ( 2p + 1 ) = ( 5p + 5 ) - 10
⇒ 10 - 2p - 1 = 5p + 5 - 10
⇒ 10 - 1 - 5 + 10 = 5p + 2p
⇒ 5p + 2p = 10 - 1 - 5 + 10
⇒ 7p = 9 + 5
⇒ 7p = 14
⇒ p = 14 ÷ 7
⇒ p = 2
∴ The value of p is 2.
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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 AP.
5. Formula for sum of the first n terms of AP:
- Sₙ = n / 2 [ 2a + ( n - 1 ) * d ]
10-(2p+1)=5p+5-10
9-2p=5p-5
7p=14
p=2
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