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#