What is the sum of the geometric sequence 2, 10, 50, … if there are 7 terms?
Sn = a1 (r^n - 1)
----------
r - 1
S10 = 2 * (5^7 - 1)
---------- = 39062
5 - 1
Answer: The sum of the given G.P is 39062
Step-by-step explanation:
Since, the sum of a G.P. is,
\(S_{n}=\frac{a(r^n-1)}{r-1}\)
( If r > 1 )
Where r is the common ratio, a is the first term and n is the number of terms.
Here, the given G.P. is,
2, 10, 50, … up to 7 terms
⇒ a = 2, r = 5 and n = 7,
Thus, the sum of this series,
\(S_{7}=\frac{2(5^7-1)}{5-1}\)
\(=\frac{2(78125-1)}{4}\)
\(=\frac{156248}{4}=39062\)