Question

A3+a6=10, s10=60 d=?

Answer 1

Ответ d= 1.

Решение задания приложено

Answer 2

To find the value of 'd' in the arithmetic sequence, we can use the formulas related to arithmetic sequences. Let's break down the given information and use the formulas to find the value of 'd.'

The arithmetic sequence is defined by the formula:

an = a1 + (n - 1)d,

where 'an' represents the nth term, 'a1' is the first term, 'n' is the position of the term in the sequence, and 'd' is the common difference between consecutive terms.

Given information: a3 + a6 = 10 (sum of the third and sixth terms) s10 = 60 (sum of the first ten terms)

We'll start by finding the value of 'a1' using the formula for the sum of an arithmetic series:

s10 = (n/2)(2a1 + (n - 1)d),

Substituting the given values: 60 = (10/2)(2a1 + (10 - 1)d), 60 = 5(2a1 + 9d), 12 = 2a1 + 9d.

Now, let's use this information to find the value of 'd.'

We'll substitute 'a1 + 2d' for 'a3' and 'a1 + 5d' for 'a6' in the equation 'a3 + a6 = 10':

(a1 + 2d) + (a1 + 5d) = 10, 2a1 + 7d = 10.

We now have a system of equations:

2a1 + 7d = 10, (Equation 1) 2a1 + 9d = 12. (Equation 2)

Subtracting Equation 1 from Equation 2 will eliminate 'a1':

(2a1 + 9d) - (2a1 + 7d) = 12 - 10, 2d = 2, d = 1.

Therefore, the value of 'd' is 1 in the given arithmetic sequence.