Question

А1 = 3, а75 = 299. Знайти а50.

Answer 1

Арифметическая прогрессия: а(n)=a(1)+d(n-1)
a(75)=3+d(75-1)
299=3+74d.
74d=296
d=4
a(50)=3+4(50-1)
a(50)=199

Answer 2

To find the value of a50, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1) * d

where: an is the nth term, a1 is the first term, n is the position of the term we want to find, d is the common difference between consecutive terms.

In this case, we are given that a1 = 3 and a75 = 299.

Let's calculate the common difference (d) first:

d = a2 - a1 = a3 - a2 = ... = a75 - a74

Since it's an arithmetic sequence, the difference between consecutive terms remains constant. We can calculate d using the given values:

d = a75 - a74 d = 299 - a1 d = 299 - 3 d = 296

Now, let's find a50 using the formula:

a50 = a1 + (50 - 1) * d a50 = 3 + 49 * 296 a50 = 3 + 14504 a50 = 14507

Therefore, a50 is equal to 14507.