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The nth term (tn) of a certain sequence is defined as tn = t

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Bunuel
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The nth term (tn) of a certain sequence is defined as tn = t [#permalink] New post   Updated on: 30 Dec 2022, 10:50
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The \(n_{th}\) term (\(t_n\)) of a certain sequence is defined as \(t_{n}\) = \(t_{n-1}\) \(+4\). If \(t_{1}\) =−7 then \(t_{71} =\)

A. 273
B. 277
C. 281
D. 283
E. 287

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A

Originally posted by Bunuel on 04 Dec 2017, 05:24.
Last edited by Carcass on 30 Dec 2022, 10:50, edited 1 time in total.
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Re: The nth term (tn) of a certain sequence is defined as tn = t [#permalink] New post   04 Dec 2017, 12:54
Bunuel wrote:
The \(n_{th}\) term (\(t_n\)) of a certain sequence is defined as \(t_{n}\) = \(t_{n-1}\) \(+24\). If \(t_{1}\) =−7 then \(t_{71} =\)

A. 273
B. 277
C. 281
D. 283
E. 287

Kudos for correct solution.



Bunuel - is this the ques? as I have edited. Could you plz check the ques.
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jezzsk8
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Re: The nth term (tn) of a certain sequence is defined as tn = t [#permalink] New post   05 Dec 2017, 07:41
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I think it should be \(t_n\,=\,t_{n-1}\,+\,4\).

In that case, it's given that \(t_1 = -7\). The \(0th\) term would be \(-11\), and the sequence could be expressed as..

\(t_n = -11 + 4n\)

The 71th term is...

\(t_{71} = -11 + 4(71)\)

\(t_{71} = 273\).

The answer is A.
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Re: The nth term (tn) of a certain sequence is defined as tn = t [#permalink] New post   06 Dec 2017, 03:08
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jezzsk8 wrote:
I think it should be \(t_n\,=\,t_{n-1}\,+\,4\).

In that case, it's given that \(t_1 = -7\). The \(0th\) term would be \(-11\), and the sequence could be expressed as..

\(t_n = -11 + 4n\)

The 71th term is...

\(t_{71} = -11 + 4(71)\)

\(t_{71} = 273\).

The answer is A.



Yes right. thanks for that, i have edited the main question.
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Re: The nth term (tn) of a certain sequence is defined as tn = t [#permalink] New post   06 Dec 2017, 03:13
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Thank you guys. Kudos

Regards
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Re: The nth term (tn) of a certain sequence is defined as tn = t [#permalink] New post   23 Nov 2018, 05:42
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The \(n\)th term (\(t_n\)) of a certain sequence is defined as \(t_n = t_{n-1} + 4\) . If \(t_1=-7\) then \(t_{71} =\)

A. 273

B. 277

C. 281

D. 283

E. 287
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Re: The nth term (tn) of a certain sequence is defined as tn = t [#permalink] New post   23 Nov 2018, 12:18
Carcass wrote:
The \(n\)th term (\(t_n\)) of a certain sequence is defined as \(t_n = t_{n-1} + 4\) . If \(t_1=-7\) then \(t_{71} =\)

A. 273

B. 277

C. 281

D. 283

E. 287



t71 = -7 + 4(71-1) = -7 + 280 = 273

Answer choice A
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Re: The nth term (tn) of a certain sequence is defined as tn = t [#permalink] New post   03 Mar 2020, 06:20
Bunuel wrote:
The \(n_{th}\) term (\(t_n\)) of a certain sequence is defined as \(t_{n}\) = \(t_{n-1}\) \(+4\). If \(t_{1}\) =−7 then \(t_{71} =\)

A. 273
B. 277
C. 281
D. 283
E. 287

Kudos for correct solution.

If we don't already know the formula for arithmetic sequences, we can still answer the question.

The given formula tells us that each term in the sequence is 4 greater than the term before it.
So, let's list some terms to see if we can see a pattern

term1 = -7
term2 = -7 + 4
term3 = -7 + 4 + 4
term4 = -7 + 4 + 4 + 4
term5 = -7 + 4 + 4 + 4 + 4
.
.
.
At this point we can probably see the pattern

So, term71 = -7 + 4 + 4 + 4 + 4 + 4 + 4 + 4.......

QUESTION: How many 4's are in the sum for term71?
Well, term1 has 0 4's
term2 has 1 4
term3 has 2 4's
term4 has 3 4's
etc

So, we can see that term71 has 70 4's

In other words, term71 = -7 + (70)(4)
= -7 + 280
= 273

Answer: A

Cheers,
Brent
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Re: The nth term (tn) of a certain sequence is defined as tn = t [#permalink] New post   28 Mar 2021, 14:24
Carcass wrote:
The \(n\)th term (\(t_n\)) of a certain sequence is defined as \(t_n = t_{n-1} + 4\) . If \(t_1=-7\) then \(t_{71} =\)

A. 273

B. 277

C. 281

D. 283

E. 287


If we don't already know the formula for arithmetic sequences, we can still answer the question.

The given formula tells us that each term in the sequence is 4 greater than the term before it.
So, let's list some terms to see if we can see a pattern

term1 = -7
term2 = -7 + 4
term3 = -7 + 4 + 4
term4 = -7 + 4 + 4 + 4
term5 = -7 + 4 + 4 + 4 + 4
.
.
.
At this point we can probably see the pattern

So, term71 = -7 + 4 + 4 + 4 + 4 + 4 + 4 + 4.......

QUESTION: How many 4's are in the sum for term71?
Well, term1 has 0 4's
term2 has 1 4
term3 has 2 4's
term4 has 3 4's
etc

So, we can see that term71 has 70 4's

In other words, term71 = -7 + (70)(4)
= -7 + 280
= 273

Answer: A

Cheers,
Brent
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Re: The nth term (tn) of a certain sequence is defined as tn = t [#permalink] New post   23 Sep 2021, 10:18
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