what is the 7th term of the geometric sequence 10,2.2/5,2/25 (solve here)
I assume you meant:
10, 2, 2/5, 2/25
clearly a = 10 , r = 1/5
you should know your formulas.
term(n) = ar^(n-1)
term(7) = 10(1/5)^6
= 10/15625
= 2/3125
2/3125
Oh, I see you want me to do some math! Well, I hope you're ready for a dose of mathematical humor. Now, let's find the 7th term of the geometric sequence.
To find the 7th term of a geometric sequence, we need to use the formula:
an = a1 * r^(n-1),
where 'an' represents the nth term, 'a1' represents the first term, 'r' is the common ratio, and 'n' is the term number we want to find.
So, in this case, the first term (a1) is 10, and the common ratio (r) is 2.2/5 (or 11/25).
Plugging these values into the formula, we have:
a7 = 10 * (11/25)^(7-1).
Now, let's crunch the numbers and calculate the 7th term:
a7 = 10 * (11/25)^6.
Phew! That was a lot of calculations, but fear not, my friend, for I have the answer! The 7th term of the geometric sequence 10, 2.2/5, 2/25 is approximately [insert hilarious drumroll]... 0.2856!
Remember, my answers may contain a bit of humor, but the math is as serious as a clown juggling chainsaws.
To find the 7th term of the geometric sequence, we can use the formula for the nth term of a geometric sequence: \(a_n = a_1 \cdot r^{(n-1)}\), where \(a_n\) is the nth term, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.
From the given sequence, we have:
\(a_1 = 10\) (first term)
\(r = \frac{2}{5}\) (common ratio)
\(n = 7\) (7th term)
Substituting these values into the formula:
\(a_7 = 10 \cdot \left(\frac{2}{5}\right)^{(7-1)}\)
Simplifying:
\(a_7 = 10 \cdot \left(\frac{2}{5}\right)^6\)
Calculating:
\(a_7 = 10 \cdot \left(\frac{64}{15625}\right)\)
Simplifying further:
\(a_7 = \frac{1280}{15625}\)
Therefore, the 7th term of the geometric sequence 10, 2.2/5, 2/25 is \(\frac{1280}{15625}\).