Answer:
The sum of the first 7 terms in the geometric sequence is -6558
Explanation:
s7 refers to the sum of the first 7 terms of the geometric sequence
To calculate the sum of terms, we use the sum of terms formula
We have this generally given as;
Sn = a(1-r^n)/(1-r)
a refers to the first term, given as a1 which is -4374
r is the common ratio which is 1/3
n is the number of terms, which is 7
substituting these values;
s7 = -4374(1-(1/3)^7)/(1-1/3)
s7 = -4374(1-(1/3)^7)/2/3
s7 = (3 * -4374)/2 * (1- (1/3)^7
s7 = -6561 * (1-1/2187)
s7 = -6561 * (2187-1)/2187
= -6561 * 2186/2187
= -6558