Question

Помогите решить, пожалуйста. Дано: А.П a3 = 5 a7 = 13 Найти: a1 - ? S10 - ?

Answer 1

А3=а1+2d=5
a7=a1+6d=13
4d=8
d=2
a1+4=5
a1+12=13
a1=1
a10=a1+9d=1+18=19
S10=1+19/2 *10= 100

Answer 2

Problem Statement

You are given the following information: - A.P. (Arithmetic Progression) with a common difference of 3: a3 = 5 and a7 = 13.

You need to find: - a1 - ? - S10 - ?

Solution

To find the value of a1, we can use the formula for the nth term of an arithmetic progression:

an = a1 + (n - 1)d

where: - an is the nth term of the arithmetic progression - a1 is the first term of the arithmetic progression - d is the common difference of the arithmetic progression

We are given that a3 = 5 and a7 = 13. Let's substitute these values into the formula to find a1:

a3 = a1 + (3 - 1)d 5 = a1 + 2d

a7 = a1 + (7 - 1)d 13 = a1 + 6d

We have a system of two equations with two variables (a1 and d). We can solve this system of equations to find the values of a1 and d.

Subtracting the first equation from the second equation, we get:

13 - 5 = (a1 + 6d) - (a1 + 2d) 8 = 4d d = 2

Substituting the value of d back into the first equation, we can solve for a1:

5 = a1 + 2(2) 5 = a1 + 4 a1 = 1

Therefore, a1 = 1.

Now, let's find the sum of the first 10 terms of the arithmetic progression (S10). We can use the formula for the sum of an arithmetic progression:

Sn = (n/2)(2a1 + (n - 1)d)

where: - Sn is the sum of the first n terms of the arithmetic progression

Substituting the values of a1 = 1, d = 2, and n = 10 into the formula, we can find S10:

S10 = (10/2)(2(1) + (10 - 1)(2)) S10 = 5(2 + 9(2)) S10 = 5(2 + 18) S10 = 5(20) S10 = 100

Therefore, S10 = 100.

Answer

Based on the given information, we have found the following values: - a1 = 1 - S10 = 100