A gardener is recording the number of flower pots arranged each day along a pathway for a landscape project. Over six consecutive days, the number of pots placed is as follows:
5, 20, 51, 106, ?, 320

Based on the pattern observed, how many flower pots did the gardener place on the fifth day?
(a) 176
(b) 183
(c) 190
(d) 193

Question

A gardener is recording the number of flower pots arranged each day along a pathway for a landscape project. Over six consecutive days, the number of pots placed is as follows:
5, 20, 51, 106, ?, 320

Based on the pattern observed, how many flower pots did the gardener place on the fifth day?
(a) 176
(b) 183
(c) 190
(d) 193

ONLiNE UPSC · Accepted Answer

Given sequence:
5, 20, 51, 106, ?, 320
Now, find first-level differences:
20 &minus; 5 = 15
51 &minus; 20 = 31
106 &minus; 51 = 55
Now, find second-level differences:
31 &minus; 15 = 16
55 &minus; 31 = 24
&rarr; Pattern increases by +8
Continue the pattern:
Next difference = 55 + 32 = 87
&rarr; Fifth term = 106 + 87 = 193
Final check:
Sixth term = 193 + 127 = 320 (since 87 + 40 = 127)
Hence, option d is correct.

Number Patterns

Arithmetic Progression

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M Question 1	⏱ 0
A gardener is recording the number of flower pots arranged each day along a pathway for a landscape project. Over six consecutive days, the number of pots placed is as follows: 5, 20, 51, 106, ?, 320 Based on the pattern observed, how many flower pots did the gardener place on the fifth day? (a) 176 (b) 183 (c) 190 (d) 193