Proportional sequence definition, what is proportional sequence

From the second item.

an+1 an=q (same constant).

Then the number column is proportional to the series, and q is the common ratio.

A proportional sequence is a set of numbers in which each number is the same multiple of the previous number.

For example, the last number in this set of arrays is twice as large as the previous number.

2 is 2 times 1, 4 is 2 times 2 ......32 is 2 times more than 16.

This same multiple is the common ratio of the proportional series, that is, the common ratio of the proportional series is 2

Proportional sequence: A series of numbers from the second term, the ratio of each term to its previous term is equal to the same constant, this series is called the proportional sequence, and this constant is called the common ratio of the proportional sequence, denoted as q(q≠0).

The definition of a proportional sequence is a series of numbers in which the ratio of each term to its preceding term is equal to the same constant from the second term.

Proportional series refers to a series of numbers from the second term onwards, in which the ratio of each term to its predecessor is equal to the same constant, and is often represented by g and p. This constant is called the common ratio of the proportional series, which is usually represented by the letter q (q≠0), and the proportional series a1≠ 0. Each of these items is not 0.

Note: When q=1, a is a constant series.

Proportional sequences are used in life

Proportional sequences are also often used in life. For example, banks have a way to pay interest - compound interest.

That is, the interest and principal of the previous period are added together as the principal, and the interest of the next period is calculated, which is commonly referred to as "rolling interest". The formula for calculating the sum of principal and interest according to compound interest: sum of principal and interest = principal (1 + interest rate) deposit period.

As housing prices get higher and higher, many people can't pay off the house at once like this, and always have to borrow money from the bank, either to apply for a provident fund or a bank loan, but if you want to know how much principal you have to repay after a certain period of time, you can also use the number series to calculate it yourself.

As we all know, mortgage loans (CPF loans) generally pay the principal and interest in equal monthly instalments. Let's find a solution to this problem. If the loan amount is A0 yuan, the monthly interest rate of the loan is P, the repayment method is equal to the monthly repayment of principal and interest A yuan, and the principal after repayment in the Nth month is AN.

It is a series of numbers where the ratio of the latter term is the same as that of the previous term, and this ratio is called the common ratio q, such as 1, 2, 4, 8, 16....The common ratio is 2

For example, 1 3 1 9 1 27 1 81....The common ratio is 1 3 and let the general term be an (that is, the nth term), then a(n+1)=q*an, then the sum is denoted as.

sn=a1+a2+..an (1)

Multiply both sides by q, qsn=q(a1+a2+..an) =a2+a3+..an+q*an(2) [multiply q by q, and each a's corner mark will be +1].

1)-(2).

1-q)sn=q*an-a1=q*a1*q (n-1)-a1=a1(1-q n) [here an=a1*q (n-1)].

So sn=a1(1-q n) (1-q).

A proportional sequence formula is a mathematical formula for finding the sum of a certain number of proportional sequences. In addition, a proportional series where all terms are positive numbers are formed by taking the same base exponent to form an equal difference series; Conversely, if you take any positive number c as the base and use the terms of an equal difference series as an exponential power to construct can, it is an equal proportional series.

The most basic feature of an equal ratio sequence is that the sequence starts from the second term, and the ratio of each term to the previous term is a fixed value. For example, in a series, the ratio of the latter term to the previous term is 2, then this is a proportional series.

The above content refers to the Encyclopedia-Proportional Sequence Formula.

From the second term onwards, the ratio of each term to its predecessor is equal to the same constant, and this series is called a proportional series. This constant is called the common ratio of the proportional series, which is usually represented by the letter q (q≠0), and the proportional series a1≠ 0. Each of these items is not 0.

Note: When q=1, an is a constant series.

If the ratio of each term to the previous term is equal to the same constant from the second term onwards, then the series is proportional to the series.

From the second term, an+1 an=q (same constant).

Then the number column is proportional to the series, and q is the common ratio.

Let the terms a, b, and c3 in the series be proportional series.

a:a+√2

b:b+√2

c:c+√2

b^2=a*c

b 2 + 2 b * 2 = ac + (a + c) * 2 because a, b, c must be n, i.e. an integer.

So b 2 = ac

2b=a+c

a=b=c is not the same as the question.

So it is impossible for any 3 to be proportional to the series.