1.

The sum of 20 terms of the series 1 + 4 + 7 + 10 +….is:​

Answer»

GIVEN :–

• A series => 1 + 4 + 7 + 10 + ..............

TO FIND :–

• Sum of FIRST 20 TERMS = ?

SOLUTION :–

• Sum of N terms of A.P. is –

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\bf \large \implies{ \boxed{ \bf S_n = \dfrac{n}{2} \left[ 2a + (n-1)d \right]}}

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• Here –

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\bf \: \: \: {\huge{.}} \: \: \: a = 1

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\bf \: \: \: {\huge{.}} \: \: \: d = 4 - 1 = 3

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\bf \: \: \: {\huge{.}} \: \: \: n = 20

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• So that –

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\bf \implies S_{20} = \dfrac{20}{2} \left[ 2(1)+ (20-1)(3) \right]

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\bf \implies S_{20} = \cancel \dfrac{20}{2} \left[ 2+ (19)(3) \right]

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\bf \implies S_{20} = 10\left[ 2+ (19)(3) \right]

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\bf \implies S_{20} = 10(2+ 57)

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\bf \implies S_{20} = 10(59)

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\bf \implies \large{ \boxed{ \bf S_{20} = 590}}

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• Hence , Sum of 20 terms is 590.


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