The common difference of the A.P. b_{1},b_{2},.,b_{m} is 2 more than the common difference of A.P. a_{1},a_{2},,a_{n}. If a_{40} = - 159,a_{100} = - 399 and b_{100} = a_{70}, then b_{1} is equal to: Sequence & Series (Mathematics)

\begin{aligned} & a_1, a_2, \ldots, a_n \rightarrow(C D=d) \\ & b_1, b_2, \ldots, b_m \rightarrow(C D=d+2) \\ & a_{40}=a+39 d=-159 \\ & a_{100}=a+99 d=-399 \ldots(1) \end{aligned}

Subtract :

60 \mathrm{~d}=-240 \Rightarrow \mathrm{~d}=-4

using equation (1)

\begin{aligned} & a+39(-4)=-159 \\ & a=156-159=-3 \\ & a_{70}=a+69 d=-3+69(-4)=-279=b_{100} \\ & b_{100}=-279 \\ & b_1+99(d+2)=-279 \\ & b_1-198=-279 \Rightarrow b_1=-81 \end{aligned}

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