4+a+b+32+....ধারাটির সাধারণ অনুপাত কত

Solution (By Examveda Team)

Question: 4 + a + b + 32 + ... ধারাটির সাধারণ অনুপাত কত? (What is the common ratio of the sequence 4 + a + b + 32 + ...?)

Option A: 1
Option B: 2
Option C: 3
Option D: 4

Explanation:

This question is about finding the common ratio of a geometric sequence.
A geometric sequence is a sequence where each term is found by multiplying the previous term by a constant. This constant is called the common ratio.

Let's say the common ratio is 'r'. Then:
a = 4 * r (The second term 'a' is the first term '4' multiplied by 'r')
b = a * r (The third term 'b' is the second term 'a' multiplied by 'r')
32 = b * r (The fourth term '32' is the third term 'b' multiplied by 'r')

We can rewrite the fourth term as 32 = (4 * r * r) * r = 4 * r³.
So, 32 = 4 * r³

Now, divide both sides by 4:
8 = r³

To find 'r', we need to find the cube root of 8.
The cube root of 8 is 2 because 2 * 2 * 2 = 8.

Therefore, the common ratio (r) is 2.

Correct Answer: B (2)