$0.25+1+4+16+64$
Enter the values used in finding a partial sum.
$r=4 \quad a_1=0.25 \quad n=\square$
Answer (1)
To find the partial sum of the series given by the sequence 0.25 + 1 + 4 + 16 + 64 , we can analyze it as a geometric sequence.
A geometric sequence is one where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio r .
Identify the terms of the sequence :
The sequence provided is 0.25 , 1 , 4 , 16 , 64 .
Determine the first term a 1 :
The first term a 1 is given as 0.25 .
Find the common ratio r :
To find the common ratio, divide the second term by the first term: r = 0.25 1 = 4
We can check this by confirming that each subsequent term maintains this ratio: 1 4 = 4 , 4 16 = 4 , 16 64 = 4
Count the number of terms n :
The series has the terms 0.25 , 1 , 4 , 16 , 64 . Thus, there are 5 terms.
In conclusion, the values used in finding the partial sum are r = 4 , a 1 = 0.25 , and n = 5 .
