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06 Dec 2023, 02:30
Kudos
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E
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Difficulty:
95%
(hard)
Question Stats:
29% (02:27) correct
71%
(02:01)
wrong
based on 139
sessions
History
Date
Time
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Not Attempted Yet
In the sequence T, the first term is the non-zero number a, and each term after the first term is equal to the non-zero number r multiplied by the previous term. What is the value of the fourth term of the sequence?
(1) The sum of the first 2 terms of the sequence is 16.
(2) The 18th term of the sequence is 81 times the 14th term of the sequence.
(1) The sum of the first 2 terms of the sequence is 16.
(2) The 18th term of the sequence is 81 times the 14th term of the sequence.
10 Dec 2023, 19:02
Kudos
Bookmarks
In the sequence T, the first term is the non-zero number a, and each term after the first term is equal to the non-zero number r multiplied by the previous term. What is the value of the fourth term of the sequence?
The above talks of a Geometric progression a, ar, ar^2…..
(1) The sum of the first 2 terms of the sequence is 16.
\(a+ar=16\)
a could be 1 and r, 16 or a could be 4 and r could be 3.
Insufficient
(2) The 18th term of the sequence is 81 times the 14th term of the sequence.
Thus \(ar^{17}=81*ar^{13}……r^4=81\)
Thus r =3 or -3.
Insufficient
Combined
Two possibilities
\(a+3a=16……a=4\)…4, 12, 36…
\(a-3a=16…..a=-8\)…-8, 24, ….
Insufficient
The above talks of a Geometric progression a, ar, ar^2…..
(1) The sum of the first 2 terms of the sequence is 16.
\(a+ar=16\)
a could be 1 and r, 16 or a could be 4 and r could be 3.
Insufficient
(2) The 18th term of the sequence is 81 times the 14th term of the sequence.
Thus \(ar^{17}=81*ar^{13}……r^4=81\)
Thus r =3 or -3.
Insufficient
Combined
Two possibilities
\(a+3a=16……a=4\)…4, 12, 36…
\(a-3a=16…..a=-8\)…-8, 24, ….
Insufficient
