Question

Дана арифметическая прогрессия (Аn)сумма пяти ее первых членов равна 15 разность равна 2 . Найти первый член прогрессии

Answer 1

A1+a2+a3+a4+a5=a1+a1+d+a1+2d+a1+3d+a1+4d=5a1+10d=15
d=2   5a1=15-20=-5    a1= -1

Answer 2

Understanding the problem

We are given an arithmetic progression (AP) where the sum of the first five terms is equal to 15 and the common difference is 2. We need to find the first term of the progression.

Arithmetic Progression (AP)

An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. The general form of an arithmetic progression is: A, A + d, A + 2d, A + 3d, ...

In this case, we are given that the common difference (d) is 2.

Finding the first term (A)

To find the first term (A) of the arithmetic progression, we can use the formula for the sum of the first n terms of an arithmetic progression:

Sn = (n/2) * (2A + (n-1)d)

Where Sn is the sum of the first n terms, A is the first term, d is the common difference, and n is the number of terms.

In this case, we are given that the sum of the first five terms (Sn) is 15. Therefore, we can substitute the given values into the formula and solve for A.

15 = (5/2) * (2A + (5-1) * 2)

Simplifying the equation:

15 = (5/2) * (2A + 8)

Multiplying both sides by 2/5 to isolate the term:

(2/5) * 15 = 2A + 8

6 = 2A + 8

2A = 6 - 8

2A = -2

A = -1

Answer

Therefore, the first term of the arithmetic progression is -1.