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Sequence S is defined as Sn = 2Sn-1 – 2. If S1 = 3, then S10 – S9 =
- a)2
- b)120
- c)128
- d)250
- e)256
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
Sequence S is defined as Sn = 2Sn-1 – 2. If S1 = 3, then S10 &nd...
We can use the formula to calculate the first 10 values of S:
S1 = 3
S2 = 2(3) – 2 = 4
S3 = 2(4) – 2 = 6
S4 = 2(6) – 2 = 10
S5 = 2(10) – 2 = 18
S6 = 2(18) – 2 = 34
S7 = 2(34) – 2 = 66
S8 = 2(66) – 2 = 130
S9 = 2(130) – 2 = 258
S10 = 2(258) – 2 = 514
S10 – S9 = 514 – 258 = 256.
S2 = 2(3) – 2 = 4
S3 = 2(4) – 2 = 6
S4 = 2(6) – 2 = 10
S5 = 2(10) – 2 = 18
S6 = 2(18) – 2 = 34
S7 = 2(34) – 2 = 66
S8 = 2(66) – 2 = 130
S9 = 2(130) – 2 = 258
S10 = 2(258) – 2 = 514
S10 – S9 = 514 – 258 = 256.
Alternatively, we could solve this problem by noticing the following pattern in the sequence:
S2 – S1 = 1 or (20)
S3 – S2 = 2 or (21)
S4 – S3 = 4 or (22)
S5 – S4 = 8 or (23)
S2 – S1 = 1 or (20)
S3 – S2 = 2 or (21)
S4 – S3 = 4 or (22)
S5 – S4 = 8 or (23)
We could extrapolate this pattern to see that S10 – S9 = 28 = 256.
The correct answer is E
Most Upvoted Answer
Sequence S is defined as Sn = 2Sn-1 – 2. If S1 = 3, then S10 &nd...
To find the explicit formula for the sequence S, we need to know the value of the first term, S₁. Without that information, we cannot determine the explicit formula.
Please provide the value of S₁, or any other information about the sequence, so that we can help you find the explicit formula.
Please provide the value of S₁, or any other information about the sequence, so that we can help you find the explicit formula.
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Sequence S is defined as Sn = 2Sn-1 – 2. If S1 = 3, then S10 – S9 =a)2b)120c)128d)250e)256Correct answer is option 'E'. Can you explain this answer?
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