Answer:
The sum of the first 10 terms is 4092
Step-by-step explanation:
We can use the formula for a partial sum of a geometric series of first [tex]a_1[/tex] term and common ratio r, which is given by:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]
Therefore, in this particular case where we add the first 10 terms of a geometric series with first term 4 and the common ratio 2, we have:
[tex]S_n=\frac{a_1(1-r^n)}{1-r} \\S_10=\frac{4(1-2^{10})}{1-2} \\S_10=\frac{4(1-1024)}{1-2}\\S_10=\frac{4(-1023)}{-1}\\S_10=\frac{-4092)}{-1}\\S_10=4092[/tex]
Answer:
The sum of the 10 terms of geometric series is 4092
Explanation:
Given in the question, the series that will be formed is in Geometric Progression (GP) is the common ratio is mentioned here
According to GP, the sum of a series is given by the formula;
[tex]\mathrm{S}_{\mathrm{n}}=\frac{a\left(r^{n}-1\right)}{r-1}[/tex]
Then, according to question,
a is given as 4, n is given as 10 and r is given as 2.
[tex]\mathrm{S}_{10}=\frac{4\left(2^{10}-1\right)}{2-1}[/tex]
= [tex]\frac{4(1024-1)}{1}[/tex]
= 4(1023)= 4092
Therefore, the sum of the 10 terms of geometric series is 4092
