Question

Знайдіть суму :1)перших п'яти членів геометричної прогресії(bn):якщоb1=8,q=1/2;

Answer 1

Sn=(b1*(q^n-1))/(q-1);
S5=(8*(1/2)^5-1)/(1/2-1)=(8*(1/32-1))/(-1/2)=8*(-31/32)*(-2)=31/2=15,5

Answer 2

Finding the sum of the first five terms of a geometric progression

To find the sum of the first five terms of a geometric progression, we need to know the first term (b1) and the common ratio (q). In this case, we have b1 = 8 and q = 1/2.

The formula to find the sum of the first n terms of a geometric progression is given by:

Sn = b1 * (1 - q^n) / (1 - q)

Where Sn is the sum of the first n terms, b1 is the first term, q is the common ratio, and n is the number of terms.

Now, let's substitute the values into the formula and calculate the sum of the first five terms.

b1 = 8, q = 1/2, n = 5

S5 = 8 * (1 - (1/2)^5) / (1 - 1/2)

Simplifying the expression:

S5 = 8 * (1 - 1/32) / (1/2)

S5 = 8 * (31/32) / (1/2)

S5 = 8 * 31 / (32/2)

S5 = 248 / 16

S5 = 15.5

Therefore, the sum of the first five terms of the geometric progression with b1 = 8 and q = 1/2 is 15.5.