Find the 11th term

Algebra Level pending

The sum of the terms of an arithmetic progression is 1890 1890 . If it has 21 21 terms, find the 1 1 t h 11^{th} term.


The answer is 90.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Relevant wiki: Arithmetic Progression Sum

Formula: s = n 2 ( a 1 + a n ) s=\dfrac{n}{2}(a_1+a_n)

1890 = 21 2 ( a 1 + a 21 ) 1890=\dfrac{21}{2}(a_1+a_{21})

a 1 + a 21 = 180 a_1+a_{21}=180

Since the 1 1 t h 11^{th} term is the middle term of this progression, the 1 1 t h 11^{th} term is the average of the first and the last term. We have

a 11 = a 1 + a 21 2 = 180 2 = 90 a_{11}=\dfrac{a_1+a_{21}}{2}=\dfrac{180}{2}=\boxed{90}

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