A) an arithmetic progression
B) a geometric progression
C) a harmonic progression
D) an arithmetico-geometric progression
Correct Answer: B
Solution :
Given, \[{{a}_{0}}=p\] and \[{{a}_{n}}-{{a}_{n-1}}=r{{a}_{n-1}}\] \[\Rightarrow \] \[{{a}_{n}}={{a}_{n-1}}(r+1)\] For \[n=1,\,\,{{a}_{1}}={{a}_{0}}(r+1)=p(r+1)\] \[n=2,{{a}_{2}}={{a}_{1}}(r+1)=p{{(r+1)}^{2}}\] \[n=3,{{a}_{3}}={{a}_{2}}(r+1)=p{{(r+1)}^{3}}\] This shows that the sequence are in a geometric progression.You need to login to perform this action.
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