Sequence and series

t is an even number in the series 1/t +3/t +5/t +.... + t-1/t

(a)Determine the number of terms in the series in terms of t

(b) Determine the sum of the series in terms of t

Guest Mar 20, 2021

#1**+2 **

(a) The formula for the number of terms in an arithmetic sequence is:

(Last Term - The term before the first term)/ over the sequence increases by

Plugging this in, we get:

\({\frac {({\frac {t-1} {t}}-{\frac {-1} {t}})} {\frac {2} {t}}}={\frac {\frac {t} {t}} {\frac {2} {t}}}={\frac {1} {\frac {2} {t}}}={\frac {t} {2}}\)

Therefore there are **t/2** terms in the sequence.

(b) The sum of an arithmetic sequence can be calculated with the formula:

Average of all terms * Number of terms.

The average of the terms in an arithmetic sequence can be found with the formula:

(First term + Last term)/2

Plugging this in, we get:

\({\frac {({\frac {1} {t}}+{\frac {t-1} {t}})} {2}={\frac {\frac {t} {t}} {2}}}={\frac {1} {2}}\)

Therefore the average of our terms is 1/2.

Finally, the sum of our terms is 1/2*t/2 =**t/4**

Solved! :)

ArithmeticBrains1234 Mar 20, 2021