Series pattern
39 + 1 x 13 = 52
52 + 2 x 13 = 78
78 + 3 x 13 = 117
117 + 4 x 13 = 169
169 + 5 x 13 = 234 Should come in place of ?
Series pattern
12 x 2 = 24
24 x 3 = 72
72 x 2 = 144
144 x 3 = 432
432 x 2 = 864
Should come in place of '?'
Series pattern
600/5 + 5 = 125
125/5 + 5 = 30
30/5 + 5 = 11
Should come in place of '?'
11/5 + 5 = 7.2
7.5/5 + 5 = 6.44
6.44/5 + 5 = 6.288
1 x 1 + 1 = 2
2 x 2 + 2 = 6
6 x 3 + 3 = 21
21 x 4 + 4 = 88
88 x 5 + 5 = 445
445 x 6 + 6 = 2676 Should come in place of '?'
Series pattern
50 x 1.2 = 60,
60 x 1.25 = 75,
75 x 1.3 = 97.5,
97.5 x 1.35 = 131.625 Should come in place of '?'
131.625 x 1.4 = 184.275
184.275 x 1.45 = 267.19875
Series pattern
13 + 5, 23 + 5, 33 + 5, 43 + 5, 53 + 5
? Missing term = 43 + 5 = 69
Series Pattern
(-1)2, (-2)2, (-3)2, (-4)2
Missing term = 36 - 32 = 27
Let the four parts be (a - 3d), (a - d), (a + d) and (a + 3d).
(a - 3d) + (a - d) + (a +d ) + (a + 3d) = 124
? a = 31
Also, (a - 3d) (a + 3d) = (a - d) (a + d) - 128
? a2 - 9d2 = a2 - d2 - 128
? 8d2 = 128
? d = 4
a = 31, d = 4
So, the four parts are 19, 27, 35, 43.
Let the four parts be (a - 3d), (a - d), (a +d), (a + 3d).
From question,
(a -3d) + (a - d) + (a + b) + (a + 3d) = 20
? a = 5
Also, [(a - 3d) (a +3d)] / [(a - d) (a + d)] = 2/3
? [a2 - 9d2] / [a2 - d2] = 2/3
? [52 - 9d2] / [52 - d2] = 2/3
? d = 1
? a = 5, d = 1
So, the four parts are 2, 4, 6, 8
Let the man first save ? P in the first year.
Then, the given sequence is P + (P + 2000) + (P + 4000) + ..,
which is an AP with a = P , d = (P + 2000) - P = 2000,
n = 10, Sn = 145000
Sn = n/2[2a + (n - 1)d]
? 145000 = 10/2 [2 x P + 9 x 2000] = 5 [2P + 18000]
? 2P + 18000 = 145000/5 = 29000
? 2P = 29000 - 18000
? 2P = 11000
? P = ? 5500
So, the man save ? 5500 in the first year .
Here, the 1st AP is (1 + 6 + 11 + ...)
and 2nd AP is (4 + 5 + 6 + ...)
1st AP = (1 + 6 + 11 + ..)
Here , common difference = 5 and the number of terms = 100
? Sum of series = S1 = n/2[2a + (n - 1)d]
= 100/2 [2 x 1 + (100 - 1) x 5 ]
= 50[2 + 99 x 5 ]
= 50 x 497
= 24850
2nd AP = (4 +5 + 6 + ...)
Here, common difference = 1
and number of terms = 100
S2 = 100/2[2 x 4 + 99 x 1]
= 50 x 107 = 5350
? Sum of the given series
= S1 + S2 = 24850 + 5350
= 30200
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