Question

двенадцатый член арифметической прогрессии {a n} равен 1,7 а семнадцатый член равен 1,2.Найдите первый член и разность этой арифметической прогрессии пожалуйста,кто-нибудь помогииииите

Answer 1

Разность арифметической прогрессии: 
      $~~~d= \dfrac{a_n-a_m}{n-m} = \dfrac{a_{17}-a_{12}}{17-12} = \dfrac{1.2-1.7}{5} =-0.1$

Пользуясь формулой n-го члена арифметической прогрессии имеем, что
  $a_{12}=a_1+11d$   откуда    $a_1=a_{12}-11d=1.7+1.1=2.8$

Answer 2

Arithmetic Progression Problem

To find the first term and the common difference of an arithmetic progression, we can use the given information about the 12th and 17th terms.

Let's denote the first term of the arithmetic progression as 'a' and the common difference as 'd'.

Given: - The 12th term is 1.7 - The 17th term is 1.2

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

nth term = a + (n - 1)d

Using this formula, we can set up two equations using the given information:

Equation 1: 12th term = a + (12 - 1)d = 1.7 Equation 2: 17th term = a + (17 - 1)d = 1.2

Now, let's solve these equations to find the values of 'a' and 'd'.

Solving Equation 1: a + 11d = 1.7

Solving Equation 2: a + 16d = 1.2

To eliminate 'a', we can subtract Equation 1 from Equation 2:

(a + 16d) - (a + 11d) = 1.2 - 1.7 5d = -0.5 d = -0.5/5 d = -0.1

Now that we have the value of 'd', we can substitute it back into Equation 1 to find 'a':

a + 11(-0.1) = 1.7 a - 1.1 = 1.7 a = 1.7 + 1.1 a = 2.8

Therefore, the first term of the arithmetic progression is 2.8 and the common difference is -0.1.

Please let me know if you need any further assistance!