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

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Solution

The given series is 2×4+4×6+6×8+…+n terms.

n th = a n , can be clearly observed from the series.

a n =2n×(2n+2)=4 n 2 +4n (1)

Substitute 20 for n in equation (1).

a 20 =4 ( 20 ) 2 +4( 20 ) =4( 400 )+80 =1600+80 =1680

Thus, the 20th term of the series 2×4+4×6+6×8+…+n is 1680.

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20^{t h}

2 \times 4 + 4 \times 6 + 6 \times 8 + . . . . + n

20^{t h}

2 \times 4 + 4 \times 6 + 6 \times 8 + . . . + n

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

Find the 20 $^{t h}$ term and the sum of 20 terms of the series :

$2 \times 4 + 4 \times 6 + 6 \times 8 + . . . .$

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