What is gp and hp
What is gp and hp
Geometic progression ( gp) A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term, i.e.,
where r common ratio a1 first term a2 second term a3 third term an-1 the term before the n th term an the n th term
The geometric sequence is sometimes called the geometric progression or GP, for short.
The formula applied to calculate sum of first n terms of a GP: Sn = a(r^n - 1)/(r-1)
HARMONIC PROGRESSION (HP)
A harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression.
Now, we need to generate this harmonic progression. We even have to calculate the sum of the generated sequence.
1. Generating of HP or 1/AP is a simple task. The Nth term in an AP = a + (n-1)d. Using this formula, we can easily generate the sequence.
2. Calculating the sum of this progression or sequence can be a time taking task. We can either iterate while generating this sequence or we could use some approximations and come up with a formula which would give us a value accurate up to some decimal places. Below is an approximate formula.
Sum = 1/d (ln(2a + (2n – 1)d) / (2a – d))
A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term, i.e.,
| where | r | common ratio |
| a1 | first term | |
| a2 | second term | |
| a3 | third term | |
| an-1 | the term before the n th term | |
| an | the n th term |
The geometric sequence is sometimes called the geometric progression or GP, for short.
The formula applied to calculate sum of first n terms of a GP: Sn = a(r^n - 1)/(r-1)
HARMONIC PROGRESSION (HP)
A harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression.
Now, we need to generate this harmonic progression. We even have to calculate the sum of the generated sequence.
1. Generating of HP or 1/AP is a simple task. The Nth term in an AP = a + (n-1)d. Using this formula, we can easily generate the sequence.
2. Calculating the sum of this progression or sequence can be a time taking task. We can either iterate while generating this sequence or we could use some approximations and come up with a formula which would give us a value accurate up to some decimal places. Below is an approximate formula.
Sum = 1/d (ln(2a + (2n – 1)d) / (2a – d))
