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Let a1 , a2 be integers such that a1 - a2 + a3 - a4 + ........ +(-1)n-1 an = n , for n ≥ 1. Then a51 + a52 + ........ + a1023 equals
Let a1 , a2 be integers such that a1 - a2 + a3 - a4 + ........ +(-1)n-1 an = n , for n ≥ 1. Then a51 + a52 + ........ + a1023 equals
This question was asked in CAT-2019 slot 2 and options were
- -1
- 1
- 0
- 10
Please help me
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ANSWERS
1
Given that a1 - a2 + a3 - a4 + ........ +(-1) n-1 an = n
lets take n=1
So, a1 = 1
Similarly
a1 - a2 = 2 => a2 = 1-2 = -1
a1 - a2 + a3 = 3 => a3 = 1
So, the series proceeds as 1, -1, 1, -1, ...
Then a51 + a52 + ........ + a1023 = 1 + (-1) + .... + 1
a51 + a52 + ........ + a1023 = 1
Hence option 2 is correct
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