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# In the sequence T, the first term is the non-zero number a, and each..

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Director
Joined: 11 Feb 2015
Posts: 618
In the sequence T, the first term is the non-zero number a, and each..  [#permalink]

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02 Jul 2018, 08:20
1
00:00

Difficulty:

85% (hard)

Question Stats:

39% (02:23) correct 61% (02:00) wrong based on 40 sessions

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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.

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Manager
Joined: 28 Jul 2016
Posts: 134
Re: In the sequence T, the first term is the non-zero number a, and each..  [#permalink]

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02 Jul 2018, 09:26
1
1st term: $$T_1$$= $$a$$
2nd term $$T_2$$ =$$a*r$$
3rd term $$T_3$$= $$a*r*r = a*r^2$$
n-th term $$T_n$$ = $$a*r^{n-1}$$

1) $$a + a*r = 16$$
$$a*(1+r) = 16$$
We can have muptiple pairs of a and r that satisfy this equation
So Not sufficient

2) So $$18_{th}$$ term: $$T_{18}$$= $$a*r^{17}$$
$$14_{th}$$ term: $$T_{14}= a*r^{13}$$
$$\frac{T_{18}}{T_{14}} = \frac{a*r^{17}}{a*r^{13}} = r^{4} = 81$$
$$r = \pm 3$$
So Not sufficient

Both 1) and 2) don't give us uniqe combination of a and r to define $$T_4$$
If r = +3, then a = +4, $$T_4 = 64$$
If r = -3, then a = -8, $$T_4 = -0.001953125$$
So Not sufficient

Manager
Joined: 28 Jul 2016
Posts: 134
Re: In the sequence T, the first term is the non-zero number a, and each..  [#permalink]

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02 Jul 2018, 09:27
This is geometrical progression
and we use formula to find n-th element of geometrical progression
Re: In the sequence T, the first term is the non-zero number a, and each.. &nbs [#permalink] 02 Jul 2018, 09:27
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