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 term = a_n = 2n × (2n + 2) = 4n² + 4n

a₂₀ = 4 (20)² + 4(20) = 4 (400) + 80 = 1600 + 80 = 1680

Thus, the 20^th term of the series is 1680.

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