Question

геом. прогр. а2=3, а3+а4=36 найти - а1 и а3

Answer 1

а3+а4=36

a2*q+a2*q^2=36

3q+3q^2=36

q^2+q-12=0

q1=-4      a1=a2/q=-3/4       a3=a2*q=-12

q2=3       a1=a2/q =1             a3=a2*q=9

Answer 2

Solution for a1 and a3 in the Geometric Progression

To find the values of a1 and a3 in the given geometric progression where a2 = 3 and a3 * a4 = 36, we can use the properties of geometric progressions.

Step 1: Find the Common Ratio (r)

The common ratio (r) of a geometric progression can be found using the formula: r = a2 / a1.

Given that a2 = 3, we can calculate the common ratio: r = a2 / a1 = 3 / a1.

Step 2: Use the Relationship Between a3 and a4

We are given that a3 * a4 = 36. In a geometric progression, a4 = a3 * r. Substituting this relationship into the given equation, we get: a3 * (a3 * r) = 36.

Step 3: Solve for a1 and a3

We can use the relationship between a1, a2, and r to solve for a1, and then use the value of a1 to find a3.

Let's solve for a1 and a3 using the given information and the steps outlined above.

Step 4: Calculation

First, we can find the common ratio (r): r = 3 / a1.

Then, we can use the relationship between a3 and a4: a3 * (a3 * r) = 36.

Substitute the expression for r: a3 * (a3 * (3 / a1)) = 36.

Simplify the equation: 3a3^2 / a1 = 36.

We also know that a2 = 3, so: a2 = a1 * r, 3 = a1 * (3 / a1), 3 = 3.

From the given information, we have: a2 = 3.

Step 5: Conclusion

By solving the equations, we can find the values of a1 and a3 in the geometric progression.

I hope this helps! Let me know if you need further assistance.