Question

Известно, что в арифметической прогрессии a3 = 3; a5 = 4. Найдите S7

Answer 1

Если а3=3, а а5 = 4 следовательно d = 0.5
2+2,5+3+3,5+4+4,5+5=24,5

Answer 2

Arithmetic Progression and Finding S7

In an arithmetic progression, the nth term (an) is given by the formula: an = a1 + (n-1)d, where a1 is the first term and d is the common difference.

Given that a3 = 3 and a5 = 4, we can find the common difference (d) and then use it to find the seventh term (a7).

First, let's find the common difference (d): - Using the given values, we can set up the following equations: - a3 = a1 + 2d = 3 - a5 = a1 + 4d = 4

Solving these equations will give us the value of the common difference (d).

Now, let's calculate the common difference (d): - From the equation a3 = a1 + 2d = 3, we can solve for a1 in terms of d: a1 = 3 - 2d . - Substituting a1 = 3 - 2d into the equation a5 = a1 + 4d = 4, we get: 3 - 2d + 4d = 4. - Solving this equation will give us the value of the common difference (d) .

Next, we can find the value of the common difference (d) using the given information.

Now that we have the common difference (d), we can find the seventh term (a7) using the formula: a7 = a1 + 6d, where 6 is the position of the seventh term.

Finally, let's calculate the seventh term (a7) using the common difference (d) we found: - Substitute the value of d into the formula a7 = a1 + 6d to find the seventh term (a7) .

By following these steps, we can find the value of the seventh term (a7) in the given arithmetic progression.