Find the 20th term of the series 2 × 4 + 4 × 6 + 6 × 8 + … + n terms.
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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