if 2th term of an ap is 213 and the sum of its first 4 terms is 24 then waht is the sum of its first 10 terms

 

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Please find below the solution to the asked query :
$$\begin{gathered} \mathrm{Although} \mathrm{question} \mathrm{is} \mathrm{not} \mathrm{correct} \mathrm{as} \mathrm{there} \mathrm{is} \mathrm{nothing} \mathrm{like} 2\mathrm{th} \mathrm{term} \\ \mathrm{Still} \mathrm{let} \mathrm{the} \mathrm{first} \mathrm{term} \mathrm{is} \mathrm{a} \mathrm{and} \mathrm{common} \mathrm{difference} \mathrm{is} \mathrm{d} \\ \mathrm{a}+\mathrm{d}= 213.....\left(1\right) \\ \mathrm{a}+\mathrm{a}+\mathrm{d}+\mathrm{a}+2\mathrm{d}+\mathrm{a}+3\mathrm{d}= 24 \\ 4\mathrm{a}+6\mathrm{d}= 24 \\ 2\mathrm{a}+3\mathrm{d}= 12......\left(2\right) \\ \mathrm{Multiplying} \mathrm{equation} 1 \mathrm{by} 2 \mathrm{and} \mathrm{then} \mathrm{subtracting} \mathrm{from} \mathrm{equation} 2 \mathrm{we} \mathrm{get} \\ \mathrm{d} = -414 \\ \mathrm{and} \mathrm{hence} \mathrm{a}= 213-\mathrm{d} = 627 \\ \mathrm{So} {\mathrm{S}}_{10}=\frac{\mathrm{n}}{2}\left[2\mathrm{a}+\left(\mathrm{n}-1\right)\mathrm{d}\right]=\frac{10}{2}\left[2\times 627+\left(10-1\right)\times -414\right] \\ =-12360 \end{gathered}$$

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