If a_1, a_2, ..., a_{24} are in an arithmetic | vedclass

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(A) Given that $a_1, a_2, ..., a_{24}$ are in an arithmetic progression.We know that in an arithmetic progression,the sum of terms equidistant from th

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$900$

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(A) Given that $a_1, a_2, ..., a_{24}$ are in an arithmetic progression.We know that in an arithmetic progression,the sum of terms equidistant from the beginning and the end is constant and equal to the sum of the first and last terms,i.e.,$a_k + a_{n-k+1} = a_1 + a_n$.Therefore,$a_1 + a_{24} = a_5 + a_{20} = a_{10} + a_{15}$.Given $a_1 + a_5 + a_{10} + a_{15} + a_{20} + a_{24} = 225$.Substituting the property,we get $3(a_1 + a_{24}) = 225$.So,$a_1 + a_{24} = 75$.The sum of the first $n$ terms is $S_n = \frac{n}{2}(a_1 + a_n)$.For $n = 24$,$S_{24} = \frac{24}{2}(a_1 + a_{24}) = 12 	imes 75 = 900$.

If $a_1, a_2, ..., a_{24}$ are in an arithmetic progression and $a_1 + a_5 + a_{10} + a_{15} + a_{20} + a_{24} = 225$,then what is the sum of the first $24$ terms of this arithmetic progression?

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