The sum of the first 10 terms of the series is 23.
An arithmetic progression(AP) is a sequence or series of numbers such that the difference of any two successive members is a constant. The first term is a, the common difference is d, n is number of terms.
For the given situation,
The series is 0.5,0.9,1.3,1.7.....
Here the first term, a = 0.5,
The common difference, d = [tex]0.9-0.5[/tex]
⇒ [tex]d=0.4[/tex]
Number of terms, n = 10
The formula of sum of n terms is
[tex]S_{n}=\frac{n}{2} [2a+(n-1)d][/tex]
On substituting the above values,
⇒ [tex]S_{10}=\frac{10}{2} [2(0.5)+(10-1)(0.4)][/tex]
⇒ [tex]S_{10}=5 [1+9(0.4)][/tex]
⇒ [tex]S_{10}=5 [1+3.6][/tex]
⇒ [tex]S_{10}=5 [4.6][/tex]
⇒ [tex]S_{10}=23[/tex]
Hence we can conclude that the sum of the first 10 terms of the series is 23.
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