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The first term in a sequence is -20. Every consecutive term is 15 grea

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Bunuel
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The first term in a sequence is -20. Every consecutive term is 15 grea [#permalink] The first term in a sequence is -20. Every consecutive term is 15 grea   15 Jul 2020, 02:22
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The first term in a sequence is -20. Every consecutive term is 15 greater than the term that immediately preceded it. What is the value of the 120th term in the sequence?

A. 1,765
B. 1,770
C. 1,775
D. 1,780
E. 1,785
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The first term in a sequence is -20. Every consecutive term is 15 grea [#permalink] The first term in a sequence is -20. Every consecutive term is 15 grea   15 Jul 2020, 02:25
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Bunuel wrote:
The first term in a sequence is -20. Every consecutive term is 15 greater than the term that immediately preceded it. What is the value of the 120th term in the sequence?

A. 1,765
B. 1,770
C. 1,775
D. 1,780
E. 1,785


First term a = -20

Common difference, d = 15

CONCEPT: nth Term of an Arithmetic Progression, \(T_n = a+(n-1)*d\)


120th term, \(= T_{120} = (-20)+(120-1)*15 = 1765\)



Answer: Option A
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The first term in a sequence is -20. Every consecutive term is 15 grea [#permalink] The first term in a sequence is -20. Every consecutive term is 15 grea   15 Jul 2020, 02:27
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a + 119d = -20+ 119(15)
= -20 + (120-1)*15
= -20 + 1800 - 15
= 1765


Option A

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Re: The first term in a sequence is -20. Every consecutive term is 15 grea [#permalink] The first term in a sequence is -20. Every consecutive term is 15 grea   15 Jul 2020, 03:50
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Bunuel wrote:
The first term in a sequence is -20. Every consecutive term is 15 greater than the term that immediately preceded it. What is the value of the 120th term in the sequence?

A. 1,765
B. 1,770
C. 1,775
D. 1,780
E. 1,785


Solution


    • Since the difference between any two consecutive terms of the given sequence is constant.
      o So, the given sequence is in AP.
    • Now, the first term of the given A. P. (i.e. a) = -20
    • And the common difference of the given A.P. (i.e. d) = 15
    • We know that nth term of an AP is given by the formula:
      o \( a_n = a + (n-1)*d\)
    • Therefore, 120th term of the given A.P. (i.e. \(a_{120}\)) \(= -20 + (120-1)*15 = -20 + 1785 = 1765 \)
Thus, the correct answer is Option A.
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Re: The first term in a sequence is -20. Every consecutive term is 15 grea [#permalink] The first term in a sequence is -20. Every consecutive term is 15 grea   15 Jul 2020, 04:40
nth term = dn + (a - d)
Where d is the difference between the terms = 15,
a is the first term = -20
and n is the term number = 120

putting values = 15*120 + (-20-15)
120th term = 1800-35
120th term = 1765

Answer is A
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The first term in a sequence is -20. Every consecutive term is 15 grea [#permalink] The first term in a sequence is -20. Every consecutive term is 15 grea   15 Jul 2020, 06:54
Bunuel wrote:
The first term in a sequence is -20. Every consecutive term is 15 greater than the term that immediately preceded it. What is the value of the 120th term in the sequence?

A. 1,765
B. 1,770
C. 1,775
D. 1,780
E. 1,785


Given: The first term in a sequence is -20. Every consecutive term is 15 greater than the term that immediately preceded it.
Asked: What is the value of the 120th term in the sequence?

Sequence forms an arithmetic progression with : -
a = -20
n = 120
d = 15

\(t_n = t_{120} = a + (n-1)d = -20 + 119*15 = 1765\)

IMO A
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Re: The first term in a sequence is -20. Every consecutive term is 15 grea [#permalink] The first term in a sequence is -20. Every consecutive term is 15 grea   27 Apr 2024, 11:03
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Re: The first term in a sequence is -20. Every consecutive term is 15 grea [#permalink]
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