Question Number 101185 by Shazneen last updated on 01/Jul/20
$${In}\:{an}\:{arithmetic}\:{progression}\:{the}\:{sum}\:{of}\:{the}\:{third}\:{term}\:{and}\:\mathrm{8}{th}\:{term}\:{is}\:\mathrm{49}\:{and}\:{the}\:{sum}\:{of}\:{the}\:\:\mathrm{5}{th}\:{and}\:\mathrm{9}{th}\:{term}\:{is}\:\mathrm{58}.{Find}\:{the}\:{first}\:{term}\:{and}\:{the}\:{common}\:{difference}\:{using}\:{simultaneous}\:{equations}. \\ $$
Answered by $@y@m last updated on 01/Jul/20
$${a}+\mathrm{2}{d}+{a}+\mathrm{7}{d}=\mathrm{49}\:\&\:{a}+\mathrm{4}{d}+{a}+\mathrm{8}{d}=\mathrm{58} \\ $$$$\mathrm{2}{a}+\mathrm{9}{d}=\mathrm{49} \\ $$$$\mathrm{2}{a}+\mathrm{12}{d}=\mathrm{58} \\ $$$$\_\_\_\_\_\_\_\_\_ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{3}{d}=\mathrm{9} \\ $$$${d}=\mathrm{3} \\ $$$$\mathrm{2}{a}+\mathrm{9}×\mathrm{3}=\mathrm{49} \\ $$$$\mathrm{2}{a}=\mathrm{49}−\mathrm{27} \\ $$$$\mathrm{2}{a}=\mathrm{22} \\ $$$${a}=\mathrm{11} \\ $$
Commented by smridha last updated on 01/Jul/20
$$\boldsymbol{{thats}}\:\boldsymbol{{not}}\:\boldsymbol{{true}}.. \\ $$$$\boldsymbol{{ans}}: \\ $$$$\boldsymbol{{a}}=\mathrm{11}\:\boldsymbol{{and}}\:\boldsymbol{{d}}=\mathrm{3} \\ $$
Commented by Rasheed.Sindhi last updated on 01/Jul/20
$$\:\$@{y}@{m}\:{sir}\:{you}'{ve}\:{mistakenly} \\ $$$${add}\:{instead}\:{to}\:{subtract}... \\ $$$${Are}\:{you}\:{old}\:\:'{s}@{ty}@{m}'? \\ $$
Commented by $@y@m last updated on 01/Jul/20
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Commented by bemath last updated on 01/Jul/20
$$\mathrm{hahaha}....\mathrm{i}'\mathrm{m}\:\mathrm{young}\:\mathrm{boy}\:\mathrm{too} \\ $$
Answered by Dwaipayan Shikari last updated on 01/Jul/20
$${suppose}\:{a}\:{is}\:{first}\:{term}\:{d}\:\:{is}\:{the}\:{common}\:{difference} \\ $$$${so}\:{a}+\mathrm{2}{d}+{a}+\mathrm{7}{d}=\mathrm{49}\:\:\:\Rightarrow\mathrm{2}{a}+\mathrm{9}{d}=\mathrm{49} \\ $$$$ \\ $$$$\:\:{a}+\mathrm{4}{d}+{a}+\mathrm{8}{d}=\mathrm{58}\Rightarrow\mathrm{2}{a}+\mathrm{12}{d}=\mathrm{58} \\ $$$$\mathrm{3}{d}=\mathrm{9}\Rightarrow{d}=\mathrm{3} \\ $$$${a}=\mathrm{11} \\ $$