Find the 10 th term of the following geometric sequence. 5 , 15 , 45 , 135 , …

The answer is 98,415

Step-by-step explanation:

This is because the pattern is to multiply by 3, when you keep on multiplying the term by 3 to get the next term until you get to the 10th term, the answer is 98,415.

T10  = 98415

Step-by-step explanation:

The nth term of a GP series is Tn = ar^(n-1), where a = first term and r = common ratio .The general form of a GP is a, ar, ar^2, ar^3 and so on

T10 = ar^(10-1)  = ar^9

here,

first term, a = 5

Common ratio, r determines how the next term varies in accordance with previous term

Getting the common ratio is by  saying that

         second term / first term = third term / second term

                        15    /     5          =  45           /   15

                         3                       =           3    

 => r = 3

Putting the values of a =5, r=3 in the formula T10 = ar^9

=> T10 = (5)(3)^9 (There was first of all problem of multiplication here)

           = 5*19683

    T10  = 98415

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.