The question is incomplete. Here is the complete question:
To get the next term in the sequence,multiply the last term by 2.5 . What is the value of the next term?
1 , 2.5 , 6.25, 15.625, ...
Answer:
39.0625
Step-by-step explanation:
Let the next term of the sequence be
Given:
The terms of the given sequence are 1, 2.5, 6.25, 15.625,..
Here, we can conclude that the next term is obtained by multiplying the previous term by 2.5 and is verified below.
2.5 = 1 2.5 = 2.5
6.25 = 2.5 2.5 = 6.25
15.625 = 6.25 2.5 = 15.625
Therefore, the next term is given as:
Therefore, the next term of the given sequence is 39.0625.
You can focus on the two sub-triangles ABC and ACD
We know that they are both right triangles, because we're given that AC and BD are perpendicular.
The sides AB and AD are the hypothenuses of these triangles, so we know their length through the pythagorean theorem:
But since we're given , the expressions for AD and AB are actually the same expression. This proves that AD=AB, and thus that the triangle is isosceles.