Answered

The first and last terms of a 52-term arithmetic series are listed in the table. What is the sum of the series?



Term Number Term

1 1

52 154

Verified Answer :

texaschic101

sn = (n(a1 + a52)) / 2
n = 52
a1 = 1
a52 = 154

s52 = (52(1 + 154)) / 2
s52 = (52(155)) / 2
s52 = 8060/2
s52 = 4030 <==

JeanaShupp

Answer: 4030

Step-by-step explanation:

We know that sum of an arithmetic series with first term as 'a' and the last term as 'l' is given by :-

\(S_n=\frac{n}{2}(a+l)\), where n is the number of terms

In the given situation, the number of terms = 52

The first term = 1

The 52th term = 154

Then the sum of 52 terms ids given by :-

\(S_{52}=\frac{52}{2}(1+154)\\\Rightarrow\ S_{52}=(26)(155)=4030\)

Hence, the sum of the series =4030

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