Problemas
Find the sum of the first 10 terms of the following sequence.Round to the nearest hundredth if necessary. 73,65.7. 59.13. __ Sum of a finite geometric series: S_(n)=(a_(1)-a_(1)r^n)/(1-r) square
Roztwór
Álvaro
experto · Tutor durante 3 años
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Respuesta
The sum of the first 10 terms of the given sequence is 398.99.
Explicación
## Step 1The given sequence is a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.## Step 2In this case, the common ratio (r) can be found by dividing any term by its preceding term. For example,
,
, etc.## Step 3The formula for the sum of the first n terms of a geometric sequence is given as:###
where
is the sum of the first n terms,
is the first term, r is the common ratio, and n is the number of terms.## Step 4Substitute the values of
, r, and n into the formula to find the sum of the first 10 terms.