Question

Find the 11th term of the geometric sequence 6,-18,54...

Answer 1

11th term = 354294

Explanation:

The formula for the nth term of a geometric sequence is given by:

`a_(n)=a_(1)*r^(^n^-^1^)`, where

• a1 is the first term (i.e., 6 in this case),
• r is the common ratio,
• and n is the term position (e.g., 1st, 11th, etc.)

Finding the common ratio:

• We can find the common ratio by dividing two consecutive terms.

Thus, we can find r by dividing -18 by 6:

`r = -18/6\\\\r=-3`

Thus, the common ratio is -3.

Finding the 11th term:

Now we can find the 11th term by substituting 6 for a1, -3 for r, and 11 for n in the formula for the nth term of a geometric sequence:

`a_(11)=6(-3)^(^1^1^-^1^)\\\\ a_(11)=6(-3)^(^1^0^)\\\\ a_(11)=6(59049)\\\\ a_(11)=354294`

Therefore, the 11th term of the geometric sequence is 354294.