Question

Найдите S107, если a1 = 7, a107 = 903. Ответ запишите в виде числа.

Answer 1

Ответ:

48 685

Пошаговое объяснение:

$S107=\frac{7+903}{2} * 107 = \frac{910}{2} * 107 = 455*107=48 685$

Answer 2

To find the value of S107, given that a1 = 7 and a107 = 903, 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, and d is the common difference between consecutive terms.

In this case, we are given a1 = 7 and a107 = 903. We need to find the value of S107, which represents the sum of the first 107 terms of the arithmetic sequence.

To find the common difference, we can subtract a1 from a107 and divide by 106 (the number of terms between a1 and a107):

d = (a107 - a1) / (107 - 1) d = (903 - 7) / 106 d = 896 / 106 d ≈ 8.45

Now that we have the common difference, we can find the value of S107 using the formula for the sum of an arithmetic series:

Sn = (n/2)(a1 + an)

where Sn is the sum of the first n terms.

Substituting the given values, we have:

S107 = (107/2)(7 + a107)

To find a107, we can use the formula for the nth term:

a107 = a1 + (107 - 1)d a107 = 7 + 106d

Substituting this into the formula for S107, we get:

S107 = (107/2)(7 + 7 + 106d) S107 = (107/2)(14 + 106d) S107 = (107/2)(14 + 106 * 8.45) S107 ≈ (107/2)(14 + 896.3) S107 ≈ (107/2)(910.3) S107 ≈ (107 * 910.3) / 2 S107 ≈ 97479.05

Therefore, the value of S107 is approximately 97479.05.