Question
If \({x_1} = - 1\) and \({x_m} = {x_{m + 1}} + (m + 1)\) for every positive integer $m,$ then \({x_{100}}\) equals
- -5151
- -5150
- -5051
- -5050
Option: 4
Solution:
Solution:
\({x_m} + 1 = {x_m} - (m + 1)\)
\({x_2} = {x_1} - 2 = - 1 - 2 = - 3\)
\({x_3} = {x_2} - 3 = - 1 - 2 - 3 = - 6\)
Similarly,
\({x_n} = - (1 + 2 + 3 + \ldots + n) = - \frac{{n(n + 1)}}{2}\)
Hence \({x_{100}} = - \frac{{100(101)}}{2} = - 5050\)
CAT 2020 Quant questions with Solutions
- CAT 2020 Quant Question 1
- CAT 2020 Quant Question 2
- CAT 2020 Quant Question 3
- CAT 2020 Quant Question 4
- CAT 2020 Quant Question 5
- CAT 2020 Quant Question 6
- CAT 2020 Quant Question 7
- CAT 2020 Quant Question 8
- CAT 2020 Quant Question 9
- CAT 2020 Quant Question 10
- CAT 2020 Quant Question 11
- CAT 2020 Quant Question 12
- CAT 2020 Quant Question 13
- CAT 2020 Quant Question 14
- CAT 2020 Quant Question 15
- CAT 2020 Quant Question 16
- CAT 2020 Quant Question 17
- CAT 2020 Quant Question 18
- CAT 2020 Quant Question 19
- CAT 2020 Quant Question 20
- CAT 2020 Quant Question 21
- CAT 2020 Quant Question 22
- CAT 2020 Quant Question 23
- CAT 2020 Quant Question 24
- CAT 2020 Quant Question 25
- CAT 2020 Quant Question 26
- CAT 2020 Quant Question 27
- CAT 2020 Quant Question 28
- CAT 2020 Quant Question 29
- CAT 2020 Quant Question 30
- CAT 2020 Quant Question 31
- CAT 2020 Quant Question 32
- CAT 2020 Quant Question 33
- CAT 2020 Quant Question 34
- CAT 2020 Quant Question 35
- CAT 2020 Quant Question 36
- CAT 2020 Quant Question 37
- CAT 2020 Quant Question 38
- CAT 2020 Quant Question 39
- CAT 2020 Quant Question 40
- CAT 2020 Quant Question 41
- CAT 2020 Quant Question 42
- CAT 2020 Quant Question 43
- CAT 2020 Quant Question 44
- CAT 2020 Quant Question 45
- CAT 2020 Quant Question 46
- CAT 2020 Quant Question 47
- CAT 2020 Quant Question 48
- CAT 2020 Quant Question 49
- CAT 2020 Quant Question 50
- CAT 2020 Quant Question 51
- CAT 2020 Quant Question 52
- CAT 2020 Quant Question 53
- CAT 2020 Quant Question 54
- CAT 2020 Quant Question 55
- CAT 2020 Quant Question 56
- CAT 2020 Quant Question 57
- CAT 2020 Quant Question 58
- CAT 2020 Quant Question 59
- CAT 2020 Quant Question 60
- CAT 2020 Quant Question 61
- CAT 2020 Quant Question 62
- CAT 2020 Quant Question 63
- CAT 2020 Quant Question 64
- CAT 2020 Quant Question 65
- CAT 2020 Quant Question 66
- CAT 2020 Quant Question 67
- CAT 2020 Quant Question 68
- CAT 2020 Quant Question 69
- CAT 2020 Quant Question 70
- CAT 2020 Quant Question 71
- CAT 2020 Quant Question 72
- CAT 2020 Quant Question 73
- CAT 2020 Quant Question 74
- CAT 2020 Quant Question 75
- CAT 2020 Quant Question 76
- CAT 2020 Quant Question 77
- CAT 2020 Quant Question 78