Answer:
Step-by-step explanation:
We are given;
A geometric sequence;
-2,10,-50
Required to determine the nth term
The nth term in a geometric sequence is given by the formula;
where is the first term and r is the common ratio;
In this case;
r = 10 ÷ -2
= -5
Therefore;
To get the nth term in the given geometric sequence we use;
Thus, the nth term is
Answer:
Length of side of rhombus is
Step-by-step explanation:
Given Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC. We have to find the length of side of rhombus.
It is also given that AB=a and AC=b
Let side of rhombus is x.
In ΔCEF and ΔCBA
∠CEF=∠CBA (∵Corresponding angles)
∠CFE=∠CAB (∵Corresponding angles)
By AA similarity rule, ΔCEF~ΔCBA
∴ their sides are in proportion
⇒
⇒
⇒
⇒
Hence, length of side of rhombus is
