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What is the 10 th common term between the series $2+6+10+\ldots .$ and $1+6+11+\ldots . ?$
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The correct answer is:
186
Given two series are $2+6+10+14+18+22+26+30+\ldots$
and $1+6+11+16+21+26+31+\ldots$
So, series which are made to be common terms of both series is $6,26,-\mathrm{u}$
This is an A. P where $a=6, d=20$ $\begin{aligned} \therefore \mathrm{a}_{10} &=\mathrm{a}+(\mathrm{n}-1) \mathrm{d} \\ &=6+(10-1) 20=6+9 \times 20 \\ &=180+6=186 \end{aligned}$
and $1+6+11+16+21+26+31+\ldots$
So, series which are made to be common terms of both series is $6,26,-\mathrm{u}$
This is an A. P where $a=6, d=20$ $\begin{aligned} \therefore \mathrm{a}_{10} &=\mathrm{a}+(\mathrm{n}-1) \mathrm{d} \\ &=6+(10-1) 20=6+9 \times 20 \\ &=180+6=186 \end{aligned}$
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