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Let S1, S2 and S4 be the sums to the first n, 2n and 4n terms

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Let S1, S2 and S4 be the sums to the first n, 2n and 4n terms  [#permalink]

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New post 25 Nov 2019, 06:06
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Difficulty:

  65% (hard)

Question Stats:

37% (01:51) correct 63% (01:48) wrong based on 19 sessions

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Let S1, S2 and S4 be the sums to the first n, 2n and 4n terms respectively of an arithmetic progression, with a as the first term and d as the common difference. If M = 2S1 + S2 - S4, then which of the following is true?

a) M is dependent on only n and d
b) M is dependent on only d and a
c) M is dependent on only a and n
d) M is dependent on a, d and n
e) None of the above
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Let S1, S2 and S4 be the sums to the first n, 2n and 4n terms  [#permalink]

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New post 29 Nov 2019, 11:43
Sum of first n terms of an AP: S1 =(n/2)[2a + (n- 1)d]
Hence Sum of first 2n terms: S2 =(2n/2)[2a + (2n- 1)d]
Sum of first 4n terms :S4 =(4n/2)[2a + (4n- 1)d]

Now, 2S1 + S2 - S4= 2a(2n/2+2n/2-4n/2)+d{n(n-1)+n(2n-1)-2n(4n-1)} = 2a(0)+d{n(n-1)+n(2n-1)-2n(4n-1)}= dependent on only n and d
Hence, Answer = A

CaptainLevi wrote:
Let S1, S2 and S4 be the sums to the first n, 2n and 4n terms respectively of an arithmetic progression, with a as the first term and d as the common difference. If M = 2S1 + S2 - S4, then which of the following is true?

a) M is dependent on only n and d
b) M is dependent on only d and a
c) M is dependent on only a and n
d) M is dependent on a, d and n
e) None of the above

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Let S1, S2 and S4 be the sums to the first n, 2n and 4n terms   [#permalink] 29 Nov 2019, 11:43
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Let S1, S2 and S4 be the sums to the first n, 2n and 4n terms

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