Is there a formula to calculate the number of terms in arithmetic progression?

There are formulas. The formula of geometric series terms: an = a1* q (n-1); Arithmetic progression term number formula: an = a1+(n-1) * d.

I. arithmetic progression Formula

For example 1, arithmetic progression: 1, 3, 5, 7, 9;

2. Item 1:1; Last item: 9; Tolerance: 2;

3. arithmetic progression Sum: (first item+last item) * number of items/2;

4. Number of items: (last item-first item)/tolerance+1;

5. Find the first item: the last item-tolerance * (item number-1);

6. Find the last item: the first item+tolerance * (item number-1);

7. Find the tolerance: (last item-first item)/(item number-1).

Second, the formula of equal proportion series

1, and the general formula of geometric series is: an = a1* q (n-1);

2. if the general formula is transformed into an = a 1/q * q n (n ∈ n *), when q > 0, an can be regarded as a function of independent variable n, and the point (n, an) is a set of isolated points on the curve y = a 1/q * q x ..

3.n- 1 = (an/a 1) root number n times;

4.n = (an/a 1) root number n times+1.

Extended data:

Arithmetic progression's judgment

1、

(d is a constant, n

N *) or

，n

∈N*，N

≥2, d is a constant] is equivalent to

Cheng arithmetic progression.

2, equivalent to

Cheng arithmetic progression.

3.[k and b are constants, and n∈N*] is equivalent to

Cheng arithmetic progression.

4.[A and B are constants, A is not 0, n

∈N*

] equivalent to

For arithmetic progression.

Judgment of geometric series

A series, if the ratio of any last term to the previous term is the same constant (this constant is usually expressed by q), and any item in the series is not 0, that is, this series is called geometric series, where the constant q.

This is called fair proportion.

References:

Sogou Encyclopedia-arithmetic progression

References:

Sogou encyclopedia-geometric series