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# A sequence of numbers, S1, S2, S3, . . ., is defined by Sk = k2 – k fo

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Re: A sequence of numbers, S1, S2, S3, . . ., is defined by Sk = k2 – k fo [#permalink]
D.

Sk=k^2–k = K(K-1) i.e. Sum of two consecutive integers i.e. (k-1 ) & k

Sn = 110 = 11 * 10. i.e. n =11

n-1 = 10

Sn-1 = 10 * 9 = 90
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Re: A sequence of numbers, S1, S2, S3, . . ., is defined by Sk = k2 – k fo [#permalink]
Bunuel wrote:
A sequence of numbers, $$S_1$$, $$S_2$$, $$S_3$$, ..., is defined by $$S_k = k^2 – k$$ for all positive integers k. If the value $$S_n$$ is 110, what is the value of $$S_{n – 1}$$ ?

A. 132
B. 100
C. 98
D. 90
E. 72

PS21273

$$S_n = 110$$
$$110 = n^2 - n$$
$$110 = n(n-1)$$
$$n = 11$$
$$n - 1 = 10$$

$$10^2 - 10 = 90$$

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Re: A sequence of numbers, S1, S2, S3, . . ., is defined by Sk = k2 – k fo [#permalink]

Solution

Given
In this question, we are given that
• A sequence is defined by the general term $$S_k = k^2 – k$$, for all positive integers k
• The value of $$S_n$$ is 110

To find
We need to determine
• The value of $$S_{n-1}$$

Approach and Working out
As per the given definition,
• $$S_n = n^2 – n = 110$$
Or, $$n^2 – n – 110 = 0$$
Or, $$n^2 – 11n + 10n – 110 = 0$$
Or, (n – 11) (n + 10) = 0
Hence, n = 11 (as n cannot be negative)

Therefore, $$S_{n-1}$$ = $$S_{10}$$ = $$10^2 – 10$$ = 100 – 10 = 90

Thus, option D is the correct answer.

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Re: A sequence of numbers, S1, S2, S3, . . ., is defined by Sk = k2 k fo [#permalink]
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Re: A sequence of numbers, S1, S2, S3, . . ., is defined by Sk = k2 k fo [#permalink]
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