Question

if( 4/5 ,p,2) are in an A.P then find the value of p

┐( ∵ )┌step by step ​

Answer 1

Answer :

p = 7/5

Note :

★ A.P. (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are equal is said to be in A.P.

★ If a1 , a2 , a3 , . . . , an are in AP , then

a2 - a1 = a3 - a2 = a4 - a3 = . . .

★ The common difference of an AP is given by ; d = a(n) - a(n-1) .

★ The nth term of an AP is given by ;

a(n) = a + (n - 1)d .

★ If a , b , c are in AP , then 2b = a + c .

★ The sum of nth terms of an AP is given by ; S(n) = (n/2)×[ 2a + (n - 1)d ] .

or S(n) = (n/2)×(a + l) , l is the last term .

★ The nth term of an AP can be also given by ; a(n) = S(n) - S(n-1) .

Solution :

• Given : 4/5 , p , 2 are in AP
• To find : p = ?

We know that ,

If a , b , c are in AP , then 2b = a + c .

Thus ,

If 4/5 , p , 2 are in AP , then

=> 2p = 4/5 + 2

=> 2p = (4 + 10)/5

=> 2p = 14/5

=> p = 14/(5•2)

=> p = 7/5

Hence p = 7/5 .

Answer 2

Given: ⅘, p, 2 will be consecutive terms of an AP

Here, first term = ⅘

Second term= p

third term = 2

Second term - first term = third term - second term

(p) - ⅘ = 2 - p

p + p = 2 + ⅘

2p = (2× 5 +4) /5

2p = (10+4)/5

2p = 14 / 5

p = 14/(5×2)

p = 7/5

Hence, the value of p is 7/5.

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