Which term of the G.P. 4,64,1024,....G.P. 4,64,1024,....G.P. 4,64,1024,.... upto nnn terms is 262144?262144?262144?
Answer:
5th5th5th
- A geometric progression (G.P.)(G.P.)(G.P.) is of the form, a,ar,ar2,ar3,......,a,ar,ar2,ar3,......,a,ar,ar2,ar3,......, where aaa is called the first term and rrr is called the common ratio of the G.P.G.P.G.P.
The nthnthnth term of a G.P.G.P.G.P. is given by, an=arn−1an=arn−1an=arn−1 - Let 262144262144262144 be the nthnthnth term of the given G.P.,G.P.,G.P., so, we need to find the value of n.n.n.
Here, the first term, a=4a=4a=4
The common ratio, r=ak+1akr=ak+1akr=ak+1ak where k≥1k≥1k≥1
⟹r=a1+1a1=a2a1=644=16⟹r=a1+1a1=a2a1=644=16⟹r=a1+1a1=a2a1=644=16 - Now, [Math Processing Error]
- Hence, the 5th5th term of the given G.P.G.P. is 262144262144.