A sequence of numbers is called an arithmetic sequence if the difference between two consecutive terms is always the same. Put simply, this means that the next number in the series is calculated by adding a fixed number to the previous number in the series. This fixed number is called the common difference.
What are the conditions for a sequence to be an AP?
If each term of an AP is increased, decreased, multiplied, or divided by a non-zero constant number, then the resulting sequence is also in AP. If the nth n^\text{th} nth term of any sequence is of the form a n + b an + b an+b, then the sequence is in AP, where the common difference is a a a.
What is the formula of AP and GP?
The general form of an arithmetic progression is a, a + d, a + 2d, a + 3d, and so on. Thus the nth term of a series AP is Tn = a + (n 1)d, where Tn = nth term and a is = first term. Here d = common difference = T n T n 1 . The sum of n terms is also equal to the formula where l is the last term.
What is the condition of the geometric progression?
In mathematics, a geometric progression, also known as a geometric progression, is a sequence of nonzero numbers in which each term after the first is found by multiplying the previous one by a fixed nonzero number called the common ratio.
What is the condition for HP?
The simplest way to define a harmonic progression is that if the inverse of a sequence follows the rule of an arithmetic progression, then it is in a harmonic progression. This simply means if a, a+d, a+2d, ….. an A.P. then 1/a, 1/(a+d), 1/(a+2d), …… is a H.P.
How do you know if it’s arithmetic?
If you take a number in the sequence and then subtract it from the previous one and the result is still the same or constant, then it’s an arithmetic sequence. The constant difference in all pairs of consecutive or consecutive numbers in a sequence is called the common difference, denoted by the letter d.
How do I solve the progress?
The formula for the sum of the arithmetic progression is explained below:
- Consider an AP consisting of “n” terms.
- Proof: Consider an AP composed of “n” terms with the sequence a, a + d, a + 2d, …………., …
- sum composed of prime numbers is n terms = a + (a + d) + (a + 2d) + ………. …
- If we write the terms in reverse order, we get:
What is the formula for the sum of AP?
Sum of N terms of AP and arithmetic progression
| Sum of n terms of AP | n/2[2a + (n – 1)d] |
|---|---|
| Sum of natural numbers | n(n+1)/2 |
| Sum of squares of natural n Numbers | [n(n+1)(2n+1)]/6 |
| Sum of cubes of n natural numbers | [n(n+1)/2] 2 |
What is the GP formula?
Geometric progression formulas Here a is the first term and r is the common ratio. The nth term of a GP is T n = ar n 1 . Common Ratio = r = Tn / Tn 1 . The formula for calculating the sum of the first n terms of a GP is given by: Sn = a[(rn1)/(r1)] if r ≠ 1 and r > 1.
Can 0 be a GP term?
No, 0 cannot be a geometric progression term.
What is the runtime-to-runtime rule for 4 12 36?
It starts with the number 4. The next number is 12 / 4 = 3 times larger than the first. So if this sequence is geometric, the next term must be 12 3= 36. That’s true, and the next term should be 363=108, which is true.
What could HP mean?
The abbreviation HP stands for Health Points or Hit Points, Harry Potter, HP Inc., Hire Purchase and Brown Sauce. Find more information about HP here.
What is AP GP and HP?
Arithmetic Progression (AP), Geometric (GP) and Harmonic Progression (HP): CAT Quantitative Aptitude. Arithmetic progression, geometric progression, and harmonic progression are interrelated concepts and also one of the most difficult topics in the Quantitative Aptitude section of the Common Admissions Test, CAT.