Answer:
19
Step-by-step explanation:
This is a geometric series.
15, 3, (3/5), ...
common ratio r = 3/15 = (1/5)
a_1 = 15
Formula for nth term: a_n = a_1 * r^(n-1)
a_n = 15 *(1/5)^(n - 1)
We want the sum of the first 7 terms.
S = a_1 * ( r^n - 1) / (r - 1)
here let n = 7
S = 15 * ( (1/5)^7 - 1 ) / ( (1/5) - 1)
S = 15 * ( (1/5)^7 - 1) / (-4/5)
S = 15 * (5/-4) * ( (1/5)^7 - 1)
S = ( -75/4 )* (-0.9999872)
S = - (-18.74976) = 18.749...
The sum is about 19
The sum of the first 7 terms of the following series is 18.74.
'A geometric sequence is a sequence where every term has a constant ratio to its preceding term. A geometric sequence with the first term a and the common ratio r and has a finite number of terms.'
According to the given problem,
Sequence = { 15, 3, [tex]\frac{3}{5}[/tex] }
Let the common ratio be r,
Let the first term of the sequence be a,
⇒ a × r = second term
⇒ 15 × r = 3
⇒ r = [tex]\frac{3}{15}[/tex]
⇒ r = [tex]\frac{1}{5}[/tex]
We know,
Sum of n number of terms in a geometric sequence can be represented by,
[tex]S_{n} = \frac{a(1-r^{7}) }{1-r}[/tex]
⇒ [tex]S_{7} = \frac{15(1-(\frac{1}{5})^{7} ) }{1-\frac{1}{5} }[/tex]
⇒ [tex]S_{7} = \frac{15(1-(\frac{1}{5})^{7}) }{\frac{4}{5} }[/tex]
⇒ [tex]S_{7}= \frac{5*15(1-(\frac{1}{5})^{7} ) }{4}[/tex]
⇒ [tex]S_{7}= \frac{125(0.999)}{4}[/tex]
⇒ [tex]S_{7}=\frac{74}{4}[/tex]
⇒ [tex]S_{7} = 18.74[/tex]
Hence, we can conclude, the sum of the first 7 terms of the geometric sequence is 18.74.
Learn more about geometric sequence here: https://brainly.com/question/11266123
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