Final answer:
To find the sum of the first three terms of the geometric progression, divide the fourth term by the first term to find the common ratio, then use the formula for the sum of a geometric progression.
Step-by-step explanation:
To find the sum of the first three terms of the geometric progression, we need to find the common ratio of the progression. The common ratio (r) can be found by dividing the fourth term (189) by the first term (7):
r = 189/7
= 27
Now, we can find the second term (a2) by multiplying the first term (7) by the common ratio (27):
a2 = 7 * 27
= 189
The sum of the first three terms can be found using the formula for the sum of a geometric progression:
Sum = a1 + a2 + a3
= 7 + 189 + 189
= 385
Therefore, the sum of the first three terms of the geometric progression is 385.