Question

A)an=5-3n b) a3=4;a7=0 найдите S10-? Пожалуйста помогите срочно

Answer 1

$a)\;a_n=5-3n\\a_1=5-3=2\\a_{10}=5-30=-24\\S_{10}=\frac{a_1+a_{10}}2\cdot 10=(2-24)\cdot5=(-22)\cdot5=-110\\\\b)\;a_3=4,\;a_7=0\\a_3=a_1+2d\\a_7=a_1+6d\\\begin{cases}a_1+2d=4\\a_1+6d=0\end{cases}\Rightarrow\begin{cases}-4d=4\\a_1=-6d\end{cases}\Rightarrow\begin{cases}d=-1\\a_1=6\end{cases}\\S_{10}=\frac{2a_1+9d}2\cdot10=(12-9)\cdot5=15$

Answer 2

Solving for a and b:

To solve for a and b, we can use the given equations:

a3 = 4 a7 = 0

First, let's find the value of 'a': Subtracting the second equation from the first equation gives us: a7 - a3 = 0 - 4 a(7 - 3) = -4 a(4) = -4 a = -1

Now, let's find the value of 'b' using the equation an = 5 - 3n: Substitute the value of 'a' into the equation: -1n = 5 - 3n -4n = 5 n = -5/4

Now, substitute the value of 'n' into the equation to find 'b': b = 5 - 3(-5/4) b = 5 + 15/4 b = 20/4 + 15/4 b = 35/4

So, a = -1 and b = 35/4.

Finding S10:

Now that we have the values of 'a' and 'b', we can find S10 using the formula for the sum of an arithmetic series: S10 = n/2 * (2a + (n-1)d)

Where: - n = 10 (the number of terms) - a = -1 - d = 3 (the common difference)

Substitute these values into the formula: S10 = 10/2 * (2(-1) + (10-1)3) S10 = 5 * (-2 + 27) S10 = 5 * 25 S10 = 125

So, S10 = 125.