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a1, a2, a3, a4, ............ In the given sequence of numbers, each te
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29 Mar 2023, 00:21
29 Mar 2023, 00:21
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Question Stats:
72% (02:07) correct
27% (03:12) wrong based on 11 sessions
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\(a_1, a_2, a_3, a_4, ............\)
In the given sequence of numbers, each term after the first term is obtained by multiplying preceding term by 4 and subtracting 4 from the product. If the 4th term in the sequence is –4, which of the following numbers are in sequence?
Indicate all that apply
–16
0
1
5/4
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\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
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In the given sequence of numbers, each term after the first term is obtained by multiplying preceding term by 4 and subtracting 4 from the product. If the 4th term in the sequence is –4, which of the following numbers are in sequence?
Indicate all that apply
–16
0
1
5/4
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE SEQUENCES
Re: a1, a2, a3, a4, ............ In the given sequence of numbers, each te
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01 May 2023, 03:56
01 May 2023, 03:56
1
Expert Reply
OE
If 𝑎1, 𝑎2, 𝑎3, 𝑎4, 𝑎5, 𝑎6, 𝑎7,……..
,
𝑎2 = 4𝑎1 − 4 𝑎3 = 4𝑎2 − 4 𝑎4 = 4𝑎3 − 4 𝑎5 = 4𝑎4 − 4 so on…
Given the 4th term is -4.
Therefore, 𝑎5 = 4𝑎4 − 4 = 4(−4) − 4 = −20
And going backward from 𝑎5,
We know that, 𝑎4 = 4𝑎3 − 4 ⟹ 𝑎3 = a4+4/4 So a3=0
𝑎3 = 4𝑎2 − 4 ⟹ 𝑎2 = (𝑎3 + 4)/4 ⟹ 𝑎2 = 1
𝑎2 = 4𝑎1 − 4 ⟹ 𝑎1 =(𝑎1 + 4)/4⟹ 𝑎1 =5/4
And going forward from 𝑎5,
We know that, 𝑎6 = 4𝑎5 − 4 ⟹ 4(−20) − 4 = −84
𝑎7 = 4𝑎6 − 4 ⟹ 4(−84) − 4 = −340.
Further, the value decreases but we do not have any such values in the given options.
Therefore, the only values given in the option that can be a member of the given sequence is 0, 1 and 5/4.
If 𝑎1, 𝑎2, 𝑎3, 𝑎4, 𝑎5, 𝑎6, 𝑎7,……..
,
𝑎2 = 4𝑎1 − 4 𝑎3 = 4𝑎2 − 4 𝑎4 = 4𝑎3 − 4 𝑎5 = 4𝑎4 − 4 so on…
Given the 4th term is -4.
Therefore, 𝑎5 = 4𝑎4 − 4 = 4(−4) − 4 = −20
And going backward from 𝑎5,
We know that, 𝑎4 = 4𝑎3 − 4 ⟹ 𝑎3 = a4+4/4 So a3=0
𝑎3 = 4𝑎2 − 4 ⟹ 𝑎2 = (𝑎3 + 4)/4 ⟹ 𝑎2 = 1
𝑎2 = 4𝑎1 − 4 ⟹ 𝑎1 =(𝑎1 + 4)/4⟹ 𝑎1 =5/4
And going forward from 𝑎5,
We know that, 𝑎6 = 4𝑎5 − 4 ⟹ 4(−20) − 4 = −84
𝑎7 = 4𝑎6 − 4 ⟹ 4(−84) − 4 = −340.
Further, the value decreases but we do not have any such values in the given options.
Therefore, the only values given in the option that can be a member of the given sequence is 0, 1 and 5/4.
Re: a1, a2, a3, a4, ............ In the given sequence of numbers, each te
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22 Aug 2024, 23:07
22 Aug 2024, 23:07
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