What is the condition for 3 numbers to be in AP?

What is the condition for 3 numbers to be in AP?

The condition for any three numbers to be in A.P is that the common difference should be same between any two consecutive numbers. The condition for any three numbers to be in G.P is that the common ratios should be same between any two consecutive numbers.

What is the condition for harmonic progression?

Unless a = 1 and n = 1, the sum of a harmonic series will never be an integer. This is because at least one denominator of the progression is divisible by a prime number that does not divide any other denominator. Three consecutive numbers of a harmonic progression are: 1/(a–d), 1/a, 1/(a+d)

What is the condition that three non zero numbers a/b/c are in arithmetic progression?

Answer: Conditions : They should have a common difference . They should be in a proper sequence .

What is the condition for geometric progression?

Geometric Progression (GP) A sequence of numbers is called a geometric progression if the ratio of any two consecutive terms is always same. In simple terms, it means that next number in the series is calculated by multiplying a fixed number to the previous number in the series.

How can I prove 3 numbers in GP?

Let a, b and c are three consecutive elements of G.P. Then from the property of G.P’s we have common ratio = b/a = c/b. On cross multiplication, we have b² = ac. It is the important and common condition for three numbers which are consecutive elements of a G.P.

Is ABC are in AP then?

So a/bc, 1/c, 1/b are in AP. Hence option (1) is the answer.

What is the relationship between AP and GP?

A geometric progression (GP) is a sequence of numbers in which each succeeding number is obtained multiplying a specific number called common ratio. The general form of GP is: a, ar, ar2,…. A sequence of numbers is said to be a harmonic progression if the reciprocal of those numbers are in AP.

Are AB and C in arithmetic progression?

Hint: Since it is given that a, b and c are in AP, i.e. Arithmetic Progression. Therefore, we can write b as the arithmetic mean of a and c, i.e. $b=\dfrac{a+c}{2}$. So, we get a relation between a, b and c.

What is the common difference between AP and GP?

The condition is that all of them are equal. Then the common difference of AP will be 0 and common ratio of GP will be 1. If 3 terms are in AP as well as GP, what will be the values of the three terms?

How do you find the nth term of an AP?

1 nth term of an AP = a + (n-1) d 2 Arithmetic Mean = Sum of all terms in the AP / Number of terms in the AP 3 Sum of ‘n’ terms of an AP = 0.5 n (first term + last term) = 0.5 n [ 2a + (n-1) d ]

What is the sum of the terms of an AP?

Sum of ‘n’ terms of an AP = 0.5 n (first term + last term) = 0.5 n [ 2a + (n-1) d ] Geometric Progression (GP) A sequence of numbers is called a geometric progression if the ratio of any two consecutive terms is always same.

What is the formula for the general form of a GP?

Geometric Progression Formulas The general form of terms of a GP is a, ar, ar2, ar3, and so on. Here, a is the first term and r is the common ratio. The nth term of a GP is Tn = arn-1 Common ratio = r = Tn/ Tn-1 The formula to calculate the sum of the first n terms of a GP is given by: Sn = a [