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Consider a sequence of numbers given by the expression 7 + (n - 1) * 5

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Consider a sequence of numbers given by the expression 7 + (n - 1) * 5 [#permalink]

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New post 06 Oct 2014, 22:37
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Consider a sequence of numbers given by the expression 7 + (n - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?

A. 409
B. 1636
C. 16360
D. 16000
E. 15360
[Reveal] Spoiler: OA

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Re: Consider a sequence of numbers given by the expression 7 + (n - 1) * 5 [#permalink]

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New post 06 Oct 2014, 23:08
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him1985 wrote:
Consider a sequence of numbers given by the expression 7 + (n - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?

A. 409
B. 1636
C. 16360
D. 16000
E. 15360


terms in this sequence are 7,12,17----402

now since this is an a.p. with a common difference of 5. therefore its sum can be given as
n(a+l)/2----------------1)

n= total no. of terms =80
a= first term=7
l= last term=402

subsitutuing values in the expression 1 we have

80(7+402)/2
= 40(409)
=16360
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Re: Consider a sequence of numbers given by the expression 7 + (n - 1) * 5 [#permalink]

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Re: Consider a sequence of numbers given by the expression 7 + (n - 1) * 5 [#permalink]

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New post 27 Feb 2017, 05:38
n = 80
a = 7
d = 5
Sum = {n( first term + last term)}/2
= {80( 7 + 7 + 79*5)}/2
= 16360. Option C
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Re: Consider a sequence of numbers given by the expression 7 + (n - 1) * 5 [#permalink]

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New post 01 Mar 2017, 17:17
him1985 wrote:
Consider a sequence of numbers given by the expression 7 + (n - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?

A. 409
B. 1636
C. 16360
D. 16000
E. 15360


We are given the sequence 7 + (n - 1) * 5, in which n spans from 1 to 80. Let’s determine the first few values of the sequence.

n = 1

7 + (0 x 5) = 7

n = 2

7 + (1 x 5) = 12

n = 3

7 + (2 x 5) = 17

n = 4

7 + (3 x 5 ) = 22

We see that we have an evenly spaced set in which each term is 5 apart. To determine the sum, we can use the formula: sum = average x quantity. Since we know the quantity is 80, we need to determine the average.

We can use the formula: average = (first term in the set + last term in the set)/2

The last term in the set is 7 + (79 x 5) = 402, and thus:

average = (7 + 402)/2 = 409/2

Now we can calculate the sum:

sum = (409/2) x 80 = 16,360

Answer: C
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Re: Consider a sequence of numbers given by the expression 7 + (n - 1) * 5 [#permalink]

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New post 16 Mar 2017, 12:33
manpreetsingh86 wrote:
him1985 wrote:
Consider a sequence of numbers given by the expression 7 + (n - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?

A. 409
B. 1636
C. 16360
D. 16000
E. 15360


terms in this sequence are 7,12,17----402

now since this is an a.p. with a common difference of 5. therefore its sum can be given as
n(a+l)/2----------------1)

n= total no. of terms =80
a= first term=7
l= last term=402

subsitutuing values in the expression 1 we have

80(7+402)/2
= 40(409)
=16360


Kudos for the formula- I wanted to ask you- I see similar series problems on Veritasprep and wanted to ask if this formula is universal (I think it is). I have never seen this formula but now it makes a lot of sense- where did you get this formula from?
Re: Consider a sequence of numbers given by the expression 7 + (n - 1) * 5   [#permalink] 16 Mar 2017, 12:33
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