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Re: Each term of a certain sequence is 3 less than the previous term. The [#permalink]
19 .... 16.... 13 .......... 10 ......... 7.......... 4.......... 1 .......... -2 .......... -5 .......... -8 ........... -11 .......... -14............. -17

6 terms to the left of 1

6 terms to the right of 1

Total = 6+6+1 = 13

Corresponding terms addition = 4-2 = 7-5 = 10-8 = 2 .......... so on

Total = 1 + 2*6 = 13

Answer = 13
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Re: Each term of a certain sequence is 3 less than the previous term. The [#permalink]
anceer wrote:
Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 19. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?

A 1
B 13
C 15
D 19
E 47


this one can be solved logically as well..
1 definitely can't be
47 as well..as it would be way to down in the negative side..and thus n can't be negative.

now..
19, 16, 13, 10, 7, 4, 1, -2, -5, -8, -11, -14, -17, -20, -23... list all these numbers..to go further is pointless as the sum would be negative...
19-17=2
16-14=2
13-11=2
10-8=2
7-5=2
4-2=2
1
add these up = 13.
13 numbers, sum is 13. so B it is.
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Re: Each term of a certain sequence is 3 less than the previous term. The [#permalink]
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anceer wrote:
Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 19. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?

A 1
B 13
C 15
D 19
E 47


We have an arithmetic sequence, which has a general formula for the nth term as: a(n) = a(1) + d*(n - 1), where a(1) is the first term and d is the common difference. In this question, a(1) = 19 and d = -3.

We can let a(1) = 19, a(2) = 16, a(3) = 13 and so on. Therefore, the nth term, a(n) = 19 - 3*(n - 1) = 22 - 3n. Since the sequence is evenly spaced, we can use the formula: sum = average x quantity. Since the average of a finite evenly spaced sequence of n terms is [a(1) + a(n)] / 2, we have:

n = ([a(1) + a(n)] / 2) x n

n = ([19 + 22 - 3n] / 2) x n

1 = (41 - 3n) / 2

2 = 41 - 3n

3n = 39

n = 13

Answer: B
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Re: Each term of a certain sequence is 3 less than the previous term. The [#permalink]
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Re: Each term of a certain sequence is 3 less than the previous term. The [#permalink]
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