The seventh and tenth terms of a geometric sequence are 7 and 21 respectively. What is the 13th term of this progression?

63

Step-by-step explanation:

Each term in a geometric sequence progresses by multiplying a constant (let us name it r).

Let us solve for this constant r in order to find the 13th term.

If the seventh term is 7, the tenth term would be 7*r*r*r, or . We also happen to know that the 10th term is 21. Let us make a new equation:

or, approx. 1.442249570307408

Using the same logic, the 13th term would be 7*r*r*r*r*r*r, or . We may now substitute what we know, r, into this expression to obtain the 13th term:

Therefore, the 13th term of this progression is 63.

I hope this helps! Please let me know if you have any further questions :)

answer: kljdcdhjbdlchjad oac apoich a

step-by-step explanation:

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !