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85 Givena recursive searvence (an) w/a, = 2 (a2-7 & anti acn-s+8. Find a 134 + a 171
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\small \\$Given that $\\ a_1=2\\ a_2=7\\ a_{n+1}=a_{n-1}+8\\ \Rightarrow a_{n+1}-a_{n-1}=8\\ $Suppose n is a even number$\\ n=2m, ($ m is a integer$)\\ a_{2m+1}-a_{2m-1}=8\\ a_{2m-1}-a_{2m-3}=8\\ ...................................\\ a_5-a_3=8\\ a_3-a_1=8\\ $Adding we have$\\ a_{2m+1}-a_1=8\times m\\ \Rightarrow a_{2m+1}=a_1+8\times m=2+8m\\ a_{n+1}-a_{n-1}=8\\ $Suppose n is a odd number$\\ n=2p-1, ($ p is a integer$)\\ a_{2p-1+1}-a_{2p-1-1}=8\\ \Rightarrow a_{2p}-a_{2p-2}=8\\ a_{2p}-a_{2p-2}=8\\ a_{2p-2}-a_{2p-4}=8\\ ...............................\\ a_6-a_4=8\\ a_4-a_2=8\\ $Adding we have$\\ a_{2p}-a_2=8\times (p-1)\\ \Rightarrow a_{2p}=a_2+8\times (p-1)=7+8(p-1)\\ $Now we are going to find the required stuff$\\ a_{154}+a_{171}\\ =a_{2\times77}+a_{2\times85+1}\\ =7+8(77-1)+2+8(85)\\ =9+8\times76+8\times85\\ =1297

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