Question

A1=7,5 ,d=-2,5 22=...?

Answer 1

а22=а1+d.

a22=7,5-2,5=5.

Answer 2

To find the missing term, let's use the arithmetic progression formula:

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

Where: $a_n$ is the $n$th term, $a_1$ is the first term, $d$ is the common difference.

Given $a_1 = 7.5$ and $d = -2.5$, we can substitute these values into the formula:

$22 = 7.5 + (n - 1) \cdot (-2.5)$

Simplifying the equation:

$22 = 7.5 - 2.5n + 2.5$

Combining like terms:

$22 = 10 - 2.5n$

Rearranging the equation to isolate $n$:

$2.5n = 10 - 22$

$2.5n = -12$

Dividing both sides by 2.5:

$n = \frac{-12}{2.5}$

$n = -4.8$

The value of $n$ is -4.8. However, since $n$ represents the term number in the arithmetic progression, it must be a positive integer. In this case, there is no positive integer solution for $n$ that satisfies the equation.

Therefore, there is no valid term in the arithmetic progression such that $22 = \ldots$.