Question

In the arithmetic progression the first term is –30 and its difference is 2.4 Find the smallest positive term of the arithmetic progression.​

Answer 1

Ответ:

В этой задаче не может быть положительного члена. Так как идет на убывание.

Перевод:В арифметической прогрессии первый член равен –30, а его разность равна 2,4. Найдите наименьший положительный член арифметической прогрессии.

Объяснение:

Answer 2

To find the smallest positive term of the arithmetic progression with a first term of -30 and a common difference of 2.4, you can use the formula for the nth term of an arithmetic progression:

$a_n = a_1 + (n - 1) \cdot d$

Where:

• $a_n$ is the nth term.
• $a_1$ is the first term.
• $d$ is the common difference.
• $n$ is the term number we want to find.

In this case, $a_1 = -30$ and $d = 2.4$. We want to find the smallest positive term, so we are looking for the smallest positive value of $n$ for which $a_n > 0$.

Let's set up the equation:

$a_n = -30 + (n - 1) \cdot 2.4$

Now, we want to find the smallest positive $n$ for which $a_n > 0$:

$-30 + (n - 1) \cdot 2.4 > 0$

Now, we'll solve for $n$:

$(n - 1) \cdot 2.4 > 30$

Divide both sides by 2.4 to isolate $n - 1$:

$n - 1 > \frac{30}{2.4} = 12.5$

Now, add 1 to both sides to solve for $n$:

$n > 12.5 + 1 = 13.5$

Since $n$ must be a positive integer, the smallest positive term of the arithmetic progression is $n = 14$.

Now, you can find the smallest positive term by plugging $n = 14$ into the formula:

$a_{14} = -30 + (14 - 1) \cdot 2.4$

$a_{14} = -30 + 13 \cdot 2.4$

$a_{14} = -30 + 31.2$

$a_{14} = 1.2$

So, the smallest positive term of the arithmetic progression is 1.2.