Answer:
2046
Step-by-step explanation:
Formula for sum of geometric series:
\(S_{n} = a\frac{r^n - 1 }{r - 1 }\)
Where:
n = term
a = first term
r = common ratio
In this case:
a = 2
r = 2
n = ?
Formula for nth term in geometric series:
\(a_{n} = ar^{n-1}\)
\(a_{n} = 1024\)
\(1024 = 2\times2^{n-1}\)
\(1024 = 2^n\)
n = 10
Substitute in and solve.
\(S_{n} = a\frac{r^n - 1 }{r - 1} \\S_{n} = 2\frac{2^{10} - 1}{2 -1 } \\S_{n} = 2(1023) \\S_{n} = 2046\)
Thus the sum of the series is 2046.
