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03 Aug 2024, 17:45
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Difficulty:
85%
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58% (02:54) correct
42%
(03:10)
wrong
based on 66
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An arithmetic sequence has a finite number of terms and sum of all these terms is 510. If the first term of the sequence is increased by 1, the second term is increased by 3, the third term is increased by 5, and so on, then the sum of the new sequence will be 799. Find the sum of the first, last, and middle term of the original sequence.
A. 81
B. 90
C. 105
D. 120
E. 135
A. 81
B. 90
C. 105
D. 120
E. 135
03 Aug 2024, 19:08
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Option B
Sequence 1 : x, x+r, x+2r...
Sequence 2 : x+1, x+3+r, x+5+2r...
Since we are given Sum(seq-1) and Sum(seq-2) we'll use the difference
Seq-2 - Seq-1 : 1, 3, 5
Sum of above will be a perfect square representing terms in the sequence
Difference of the two sequence is 289, meaning 17 terms
Sum of an AP = n/2 * (2a+(n-1)*d)
Solving for above : a+8d = 30
Therefore a + a9 + a17 = a + a+8d + a+16d => 3*(a+8d) => 90
Posted from my mobile device
Sequence 1 : x, x+r, x+2r...
Sequence 2 : x+1, x+3+r, x+5+2r...
Since we are given Sum(seq-1) and Sum(seq-2) we'll use the difference
Seq-2 - Seq-1 : 1, 3, 5
Sum of above will be a perfect square representing terms in the sequence
Difference of the two sequence is 289, meaning 17 terms
Sum of an AP = n/2 * (2a+(n-1)*d)
Solving for above : a+8d = 30
Therefore a + a9 + a17 = a + a+8d + a+16d => 3*(a+8d) => 90
Posted from my mobile device
