find the following gp with sequence 2,8,32,128
find the sun of its 8 terms
To find the sum of the first n terms of a geometric progression (GP), we can use the formula:
Sn = a * (r^n - 1) / (r - 1)
Where:
- Sn is the sum of the first n terms,
- a is the first term of the GP,
- r is the common ratio of the GP,
- n is the number of terms we want to find the sum for.
In this case, let's find the common ratio (r) of the given GP using the given terms: 2, 8, 32, 128.
To find the common ratio (r), we can divide any term by its previous term. Let's choose the third term (32) and divide it by the second term (8):
r = 32 / 8 = 4
Now that we know the common ratio (r = 4), we can find the sum of the first 8 terms (n = 8) using the formula:
Sn = a * (r^n - 1) / (r - 1)
Substituting the values we have:
a = 2 (first term)
r = 4 (common ratio)
n = 8 (number of terms)
Sn = 2 * (4^8 - 1) / (4 - 1)
= 2 * (65,536 - 1) / 3
= 2 * 65,535 / 3
= 131,070 / 3
≈ 43,690
Therefore, the sum of the first 8 terms of the given GP is approximately 43,690.