Question

A5=18 a8=33 надо найти а1-? d-?

Answer 1

$\left \{ {{a_{8}=33 } \atop {a_{5}=18 }} \right.\\\\-\left \{ {{a_{1}+7d=33 } \atop {a_{1}+4d=18 }} \right. \\-------\\3d=15\\d=5\\a_{1}=18-4d=18-4*5=18-20=-2\\a_{1}=-2$

Answer 2

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

The formula to find the nth term of an arithmetic sequence is:

an = a1 + (n - 1) * d

Using the information given: a5 = 18 a8 = 33

We can substitute these values into the formula to create two equations:

a5 = a1 + (5 - 1) * d 18 = a1 + 4d

a8 = a1 + (8 - 1) * d 33 = a1 + 7d

We now have a system of two equations with two variables (a1 and d). We can solve this system to find the values.

Subtracting the first equation from the second equation eliminates a1:

33 - 18 = 7d - 4d 15 = 3d

Dividing both sides by 3 gives us the value of d:

d = 15 / 3 d = 5

Now, we can substitute the value of d back into one of the original equations to solve for a1:

18 = a1 + 4(5) 18 = a1 + 20 a1 = 18 - 20 a1 = -2

Therefore, the values of a1 and d are: a1 = -2 d = 5