the first term of a geometric progression is 7 while the common ratio is 3.find the 11th term?
7 * 3^10 = ___
I want to answer
To find the 11th term of a geometric progression with a first term of 7 and a common ratio of 3, we can use the formula:
nth term = first term * common ratio^(n - 1)
In this case, the first term is 7, the common ratio is 3, and we want to find the 11th term.
Let's substitute these values into the formula:
11th term = 7 * 3^(11 - 1)
Now, we can simplify this expression using exponentiation:
11th term = 7 * 3^10
To evaluate 3^10, we can break it down step by step:
3^10 = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3
After performing this multiplication, we get:
3^10 = 59,049
Now, we can substitute this value back into the formula:
11th term = 7 * 59,049
Finally, we can calculate the 11th term:
11th term = 413,343
Therefore, the 11th term of the geometric progression is 413,343.