Find the sum of the first four terms of the geometric progression (bn) given by the following conditions: b1 = 3, q = 4.

| September 9, 2021 | education

Using the definition of a geometric progression, we find successively the second, third and fourth terms of this geometric progression, and then we find the sum of the first four members of this progression.

By the condition of the problem, in a given geometric progression, b1 = 3, q ​​= 4.

Knowing the 1st term of the sequence b1 and q, we find the second term of this sequence:

b2 = b1 * q = 3 * 4 = 12.

Knowing the 2nd term of the sequence b2 and q, we find the third term of this sequence:

b3 = b2 * q = 12 * 4 = 48.

Knowing the 3rd term of the sequence b3 and q, we find the fourth term of this sequence:

b4 = b3 * q = 48 * 4 = 192.

We find the sum of the first 4 members of this sequence:

b1 + b2 + b3 + b4 = 3 + 12 + 48 + 192 = 15 + 240 = 255.

Answer: the sum of the first 4 members of this progression is 255.



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