If the first term of a finite geometric sequence is .4 and its ratio is .3 what is the sum of the first 5 terms?
You can use the formula, which I recommend, or add them up.
adding: .4,.12,.036, etc then add.
To find the sum of the first 5 terms of a finite geometric sequence, you can use the formula:
Sum = (first term * (1 - ratio^n)) / (1 - ratio),
where:
- "first term" is the first term of the sequence,
- "ratio" is the common ratio of the sequence, and
- "n" is the number of terms in the sum.
In this case, the first term is 0.4 and the ratio is 0.3. We want to find the sum of the first 5 terms, so n = 5.
Using the formula, we can substitute the values:
Sum = (0.4 * (1 - 0.3^5)) / (1 - 0.3).
Let's calculate it step by step:
Step 1: Calculate 0.3^5.
0.3^5 = 0.00243
Step 2: Calculate (1 - 0.3^5).
(1 - 0.3^5) = 0.99757
Step 3: Substitute the values into the formula:
Sum = (0.4 * 0.99757) / (1 - 0.3)
Sum = 0.398828 / 0.7
Sum = 0.56975
Therefore, the sum of the first 5 terms of the given geometric sequence is approximately 0.56975.