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Mathematics

Find the sum of first 20 terms of an A.P. whose nth term is 15 - 4n.

AP GP

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Answer

Since, an = 15 - 4n

∴ a1 = 15 - 4(1) = 15 - 4 = 11 and a20 = 15 - 4(20) = 15 - 80 = -65.

We know that

Sn=n2[a+l]∴S20=202[11+(−65)]=10[−54]=−540.Sn = \dfrac{n}{2}[a + l] \\[1em] \therefore S{20} = \dfrac{20}{2}[11 + (-65)] \\[1em] = 10[-54] \\[1em] = -540.

Hence, the sum of first 20 terms of an A.P. is -540.

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