Question

Срочно (an): a8=58; a15=16 Знайти a1 ; d.

Answer 1

A8=58;a15=16
a1;d=?
a1+7d=58
a1+14d=16

14d-7d=16-58
7d=-42
d=-42:7=-6

a1+7d=58
a1=58+42=100

Answer 2

Ответ: разность прогрессии d=(a15-a8) /7=(16-58)/7=-6. Тогда а1=а8-7*d=58+7*6=58+42=100.

Объяснение:

Answer 3

To find the values of a1 and d in the arithmetic sequence, we need to determine the common difference (d) and the first term (a1) given two specific terms.

In an arithmetic sequence, the nth term (an) can be expressed as:

an = a1 + (n - 1) * d

where: an = the nth term a1 = the first term d = the common difference between consecutive terms n = the position of the term in the sequence

We are given two specific terms: a8 = 58 (the 8th term) a15 = 16 (the 15th term)

Using the formula, we can set up two equations using these two terms:

1. For the 8th term: a8 = a1 + (8 - 1) * d 58 = a1 + 7d

2. For the 15th term: a15 = a1 + (15 - 1) * d 16 = a1 + 14d

Now, we have a system of two equations with two unknowns (a1 and d). Let's solve this system of equations:

Equation 1: 58 = a1 + 7d Equation 2: 16 = a1 + 14d

Subtract Equation 2 from Equation 1 to eliminate a1:

58 - 16 = (a1 + 7d) - (a1 + 14d) 42 = -7d

Now, solve for d:

d = -42 / -7 d = 6

Now that we have the value of d, we can find the value of a1 using either Equation 1 or Equation 2:

Using Equation 1: 58 = a1 + 7d 58 = a1 + 7 * 6 58 = a1 + 42 a1 = 58 - 42 a1 = 16

So, the first term (a1) is 16, and the common difference (d) is 6.