等差等比数列

复制import math

def arithmetic_nth(a1, d, n):
    """等差数列第 n 项：a_n = a1 + (n-1)*d"""
    return a1 + (n - 1) * d

def arithmetic_sum(a1, d, n):
    """等差数列前 n 项和：S_n = n/2 * (2*a1 + (n-1)*d)"""
    return n / 2 * (2 * a1 + (n - 1) * d)

def geometric_nth(a1, r, n):
    """等比数列第 n 项：a_n = a1 * r^(n-1)"""
    return a1 * (r ** (n - 1))

def geometric_sum(a1, r, n):
    """等比数列前 n 项和（r ≠ 1）：S_n = a1 * (1 - r^n) / (1 - r)"""
    if r == 1:
        return a1 * n
    return a1 * (1 - r ** n) / (1 - r)

# 示例：等差数列 a1=2, d=3, n=5
print("等差数列第5项:", arithmetic_nth(2, 3, 5))   # 14
print("等差数列前5项和:", arithmetic_sum(2, 3, 5)) # 40

# 示例：等比数列 a1=3, r=2, n=4
print("等比数列第4项:", geometric_nth(3, 2, 4))   # 24
print("等比数列前4项和:", geometric_sum(3, 2, 4)) # 45

复制package main

import "fmt"

func arithmeticNth(a1, d float64, n int) float64 {
	return a1 + float64(n-1)*d
}

func arithmeticSum(a1, d float64, n int) float64 {
	return float64(n) / 2.0 * (2*a1 + float64(n-1)*d)
}

func geometricNth(a1, r float64, n int) float64 {
	result := a1
	for i := 1; i < n; i++ {
		result *= r
	}
	return result
}

func geometricSum(a1, r float64, n int) float64 {
	if r == 1 {
		return a1 * float64(n)
	}
	return a1 * (1 - mathPow(r, n)) / (1 - r)
}

// 简单整数幂（避免 math.Pow 对 float64 的精度损失）
func mathPow(base float64, exp int) float64 {
	result := 1.0
	for i := 0; i < exp; i++ {
		result *= base
	}
	return result
}

func main() {
	fmt.Println("等差数列第5项:", arithmeticNth(2, 3, 5))   // 14
	fmt.Println("等差数列前5项和:", arithmeticSum(2, 3, 5)) // 40
	fmt.Println("等比数列第4项:", geometricNth(3, 2, 4))   // 24
	fmt.Println("等比数列前4项和:", geometricSum(3, 2, 4)) // 45
}

复制function arithmeticNth(a1, d, n) {
  return a1 + (n - 1) * d;
}

function arithmeticSum(a1, d, n) {
  return (n / 2) * (2 * a1 + (n - 1) * d);
}

function geometricNth(a1, r, n) {
  return a1 * Math.pow(r, n - 1);
}

function geometricSum(a1, r, n) {
  if (r === 1) return a1 * n;
  return (a1 * (1 - Math.pow(r, n))) / (1 - r);
}

console.log('等差数列第5项:', arithmeticNth(2, 3, 5));   // 14
console.log('等差数列前5项和:', arithmeticSum(2, 3, 5)); // 40
console.log('等比数列第4项:', geometricNth(3, 2, 4));   // 24
console.log('等比数列前4项和:', geometricSum(3, 2, 4)); // 45