Question

A11=6 a16=8.5 арифмет.прогрессия найти d

Answer 1

По формуле n-го члена арифм.прогрессии:
{a₁ + 15d = 8.5
{a₁ + 10d = 6
вычтем нижнее уравнение из верхнего, получим:
         5d = 2.5
           d = 2.5/5
           d = 0.5

Answer 2

To find the common difference (d) of an arithmetic progression (AP), we can use the formula:

$d = \frac{a_{n} - a_{1}}{n-1}$

where:

• $a_{n}$ is the $n$-th term of the arithmetic progression,
• $a_{1}$ is the first term of the arithmetic progression,
• $n$ is the position of the term for which we have the value.

In this case, we have the values for $a_{11}$ and $a_{16}$, and we need to find the common difference $d$.

Given: $a_{11} = 6$ and $a_{16} = 8.5$.

Let's calculate $d$ using the formula:

$d = \frac{a_{16} - a_{11}}{16-11}$ $d = \frac{8.5 - 6}{16-11}$ $d = \frac{2.5}{5}$ $d = 0.5$

Therefore, the common difference (d) of the arithmetic progression is 0.5.