An arithmetic sequence of $40$ terms is such that the sum of the even-numbered terms exceeds the s

Question

An arithmetic sequence of $40$ terms is such that the sum of the even-numbered terms exceeds the sum of the odd-numbered terms by $8$. Find the common difference; and an expression for $S_n$, the sum of the first $n$ terms, provided that $u_1 = \frac{1}{5}$.

Accepted Answer

(i) $d=\dfrac25$ (ii) $S_n=\dfrac{n^2}5$, $1\le n\le40$, $n\in\mathbb Z$

Sum of subsequence

Sum of subsequence

Solution:

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