Question

3p (p + 1)
If the sum of p terms of a series is
4
the series is an......​

Answer 1

Answer:

60

Step-by-step explanation:

= 3p(p+1)

= 3*4 (4+1)

= 12 * 5

= 60

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Answer 2

Answer :

Option (1) : A.P.

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) = a1 + (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 ] .

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

★ A linear polynomial in variable n always represents the nth term of an AP .

★ A quadratic polynomial in variable n always represents the sum of n terms of an AP .

Solution :

Here ,

The given expression for sum of p terms of a series is ;

=> S(p) = 3p(p + 1)/4

=> S(p) = 3(p² + p)/4

=> S(p) = 3p²/4 + 3p/4

Clearly ,

The polynomial S(p) is quadratic .

Thus ,

S(p) must represents the sum of p terms of an AP series .

Hence ,

The required answer is : AP .