Question

О БОГИ ЭТОГО САЙТА ПРОШУ ПОМОЩИ!!! ГЛАВНЫЕ МОЗГИ ПОМОГИТЕ ПЖ!!!! Сумма первых пяти членов арифметической прогрессии равна 80, разность прогрессии равна 3. Найдите сумму пятнадцати первых членов этой прогрессии.

Answer 1

Объяснение:

S5=(a1+a5)•5/2=(a1+a1+4d)5/2=2a1•5/2+4d•5/2=a1•5+2d•5

80=5a1+6•5;5a1=80-30; 5a1=50; a1=10

S15=(2a1+14d)•15/2; S15=(20+14•3)•15/2=62•15/2=31•15=462

Answer 2

Arithmetic Progression Sum Calculation

The sum of the first five terms of an arithmetic progression can be calculated using the formula:

Sum of first n terms (S_n) = n/2 * (2a + (n-1)d)

Where: - n = 5 (number of terms) - a = first term - d = common difference

Given that the sum of the first five terms is 80 and the common difference is 3, we can use this information to find the value of the first term (a).

Calculation Steps

1. Substitute the given values into the formula: - 80 = 5/2 * (2a + (5-1)3)

2. Solve for the first term (a): - 80 = 5/2 * (2a + 4*3) - 80 = 5/2 * (2a + 12) - 80 = 5a + 30 - 5a = 80 - 30 - 5a = 50 - a = 50 / 5 - a = 10

Now that we have found the value of the first term (a), we can proceed to find the sum of the first fifteen terms of the arithmetic progression.

Sum of the First Fifteen Terms

Using the same formula, we can calculate the sum of the first fifteen terms of the arithmetic progression with the first term (a) equal to 10 and the common difference (d) equal to 3.

Calculation Steps

1. Substitute the given values into the formula: - S₁₅ = 15/2 * (2*10 + (15-1)3)

2. Solve for the sum of the first fifteen terms (S₁₅): - S₁₅ = 15/2 * (20 + 42) - S₁₅ = 15/2 * 62 - S₁₅ = 15 * 31 - S₁₅ = 465

The sum of the first fifteen terms of this arithmetic progression is 465.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.