Answer:
Step-by-step explanation:
you can see this is a geometric progression which a ratio of [tex]{2\over{5}}[/tex]. the sum of the firs n term is:
[tex]S=a_1\frac{(1-r^n)}{(1-r)}=175\frac{1-(\frac{2}{5})^{10}}{1-\frac{2}{5}}=291.6360832[/tex]
the nearest integer would be:
292
The sum of the first 10 terms of the series 175, 70, 28, ... is 291.636
Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number. This fixed number is called common ratio.. This progression is also known as a geometric sequence of numbers that follow a pattern.
Common ratio = (Any term) / (Preceding term)
It means the sum of all the first "n" numbers in the series. The formula for first "n" natural numbers is
Sn = a + a r + ar2 + ar3 +…+ arn-1
or
Sₙ = a[(rⁿ – 1)/(r – 1)]
where "r" is called common ratio
"a" is called the first term in the series
From the given question the given series is 175, 70, 28, ...
70/175 = 0.4 (or) 28?70 = 0.4
As each succeeding term is produced by multiplying each preceding term by 0.4 .Here the common ratio (r) is 0.4
let first term "a" be 175
then Sₙ = 175[(0.4¹⁰-1)/(0.4 - 1)
Sₙ= 291.636
Thus the sum of the first 10 terms of the series 175, 70, 28, ... is 291.636
To know more about geometric progression click here
https://brainly.com/question/4853032
#SPJ2
