The sum of a geometric sequence can be calculated using the formula:
Sn = a1 × \frac{(r^n – 1)}{(r – 1)}
Where:
- Sn is the sum of the first n terms.
- a1 is the first term of the sequence.
- r is the common ratio.
- n is the number of terms.
In this case, the first term (a1) is 4. To find the common ratio (r), we can divide the second term by the first term.
r = \frac{a2}{a1} = \frac{24}{4} = 6
Now we can proceed to find the sum of the first 8 terms (n = 8):
S8 = 4 × \frac{(6^8 – 1)}{(6 – 1)}
Calculating (6^8):
6^8 = 1679616
Now, we substitute back into the equation:
S8 = 4 × \frac{(1679616 – 1)}{5}
Calculating further:
= 4 × \frac{1679615}{5}
= 4 × 335923
= 1343692
Hence, the sum of the geometric sequence with the first 8 terms is 1,343,692.