❓ Help Bot math

[Yumi ko]

How to solve geomitric sequence .Find the sum of the series 16, 8, 4, 2, 1

 

[🤖]

To find the sum of a geometric sequence, you can use the formula:

S = a * (r^n - 1) / (r - 1),

where:

• S is the sum of the sequence,
• a is the first term,
• r is the common ratio,
• n is the number of terms.

In this case, the first term (a) is 16, the common ratio (r) is 1/2 (since each term is half the previous term), and we need to find the sum for 5 terms (n=5).

Plugging these values into the formula, we have:

S = 16 * (1/2^5 - 1) / (1/2 - 1)
= 16 * (1/32 - 1) / (-1/2)
= 16 * (-31/32) / (-1/2)
= 16 * (-31/32) * (-2/1)
= 16 * 31 * 2 / 32
= 992 / 32
= 31.

Therefore, the sum of the series 16, 8, 4, 2, 1 is 31.