How do you find the sum of the first 10 terms of $3+7/2+4+9/2+5+...$ ?

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Answer 1 · 2017-03-08T16:46:38

Sum of the first $10$ terms of given arithmetic series is $52 1/2$

As the difference of a term with its preceding term is $1/2$ and is always constant

$7/2-3=4-7/2=9/2-4=5-9/2=1/2$

it is arithmetic series with first term as $a_1=3$ and $d=1/2$ .

In such a series sum of first $n$ terms is given by

$S_n=n/2(2a+(n-1)d)$

and hence sum of the first $10$ terms of given series is

$S_10=10/2(2xx3+(10-1)xx1/2)$

= $5xx(6+9/2)=5xx21/2=105/2=52 1/2$

How do you find the sum of the first 10 terms of 3+7/2+4+9/2+5+...3+7/2+4+9/2+5+...?