What is the sum of the geometric sequence 3, 18, 108 if there are 7 terms?

To find the sum of a geometric sequence, we need to use the formula:

S_n = a (1 – rⁿ) / (1 – r)

Where:

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

From the given sequence:

• a = 3
• . The second term (18) divided by the first term (3) gives us the common ratio r:
• r = 18 / 3 = 6

Now, we check the third term:

• 108 / 18 = 6, which confirms that our common ratio is correct.

Now, we want to find the sum of the first 7 terms:

S₇ = 3 * (1 – 6⁷) / (1 – 6)

Calculating 6⁷:

• 6⁷ = 279936

Now we will substitute this value back into the formula:

S₇ = 3 * (1 – 279936) / (1 – 6)

This simplifies to:

S₇ = 3 * (-279935) / (-5)

This gives us:

S₇ = 3 * 55987 = 167961

Therefore, the sum of the geometric sequence of seven terms starting with 3, 18, 108 is

167961.