Answer:
Hence, the sum of the geometric series is:
259
Step-by-step explanation:
We are given a geometric series as:
[tex]\sum_{i=1}^4 6^{i-1}[/tex]
i.e. we are asked to fnd the sum of first four terms of the geometric series with first term as 1
Since, the series is:
[tex]6^0+6^1+6^2+6^3[/tex]
Also, the common ratio of the series is: r=6
Since, each of the term of the series is 6 times it's preceding term.
Also we know that sum of a finite geometric series with n-terms and common ratio r is calculated by the formula:
[tex]S_n=a(\dfrac{r^n-1}{r-1})[/tex]
Here we have: a=1 and r=6 and n=4
Hence,
[tex]S_4=1(\dfrac{6^4-1}{6-1})\\\\\\S_4=\dfrac{1295}{5}\\\\\\S_4=259[/tex]
Hence, the sum of the series is:
259
