Question:
Find the $20^{\text {th }}$ term of the series $2 \times 4+4 \times 6+6 \times 8+\ldots+n$ terms.
Solution:
The given series is $2 \times 4+4 \times 6+6 \times 8+\ldots n$ terms
$\therefore n^{\text {th }}$ term $=a_{n}=2 n \times(2 n+2)=4 n^{2}+4 n$
$a_{20}=4(20)^{2}+4(20)=4(400)+80=1600+80=1680$
Thus, the $20^{\text {th }}$ term of the series is 1680 .
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