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In a G.P. the first, third, and fifth te...

In a G.P. the first, third, and fifth terms may be considered as the first, fourth, and sixteenth terms of an A.P. Then the fourth term of the A.P., knowing that its first term is 5, is `10` b. `12` c. `16` d. 20

A

10

B

12

C

16

D

20

Text Solution

Verified by Experts

The correct Answer is:
D
`a=5,ar^(2)=a+3d,ar^(4)=a+15d`
`therefore5r^(2)=5+3d,5r^(4)=5+15d`
`rArrr^(4)=1+3d`
`rArr25r^(4)=25+75d`
`rArr(5+3d)^(2)=25+75d`
`rArr25+30d+9d^(2)=25+75d`
`rArr9d^(2)-45d=0`
`rArrd=5,0`
`rArrT_(4)=a+3d=5+15=20`
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