Well for solving arithmetic sequences you have to add the numbers like for example if you had 2,4,6,8 The Common ratio would be 2 because you're constantly adding 2. Now for a geometric sequence it's a little different instead of adding the numbers you use multiplication to solve those ones so if the numbers were 4,16,64,256 the common ratio would be 4.
Now here comes the answers. For the matching :)
1. B Arithmetic, common difference is 2.
2. C Arithmetic, common difference is -4.
3. D Geometric, common ratio is 2.
4. A Geometric, common ratio is 0.5.
Hope This Helps You! Have A Wonderful Day. :)
Answer:

Step-by-step explanation:
Given
Sequence: 2, 6, 18, 54, 162,
Required
Determine the 15th term
The above sequence is a geometric sequence. So, first, we calculate the common ratio (r)



The 15th term is calculated as thus:

Where
and 




<em>The 15th term is 9,565,938</em>
Answer:

Step-by-step explanation:
<u>Given </u><u>:</u><u>-</u>
- A quadratic equation is given to us.
- The equation is 9x² + 30x + c .
And we need to find out the value of c for which the given trinomial is a perfect square. On looking at the given expression all the terms are having positive signs before them .So we can rewrite it on the basis of ,
<u>Identity</u><u> </u><u>:</u><u>-</u><u> </u>
Let's try to set the equation on this Identity .
The firsr term is 9x² . We can write it as ,
Hence the middle term here should contain 3 and 2 as their factors. Let's Break the middle term .

Therefore in order to make the whole expression as perfect square 5² must be replaced by c . The expression would become ,
<u>Hence </u><u>the </u><u>value </u><u>of </u><u>c </u><u>should</u><u> be</u><u> </u><u>2</u><u>5</u><u> </u><u>.</u>