All terms of an arithmetic progression are natural numbers. The sum of its nine successive terms, beginning with the first, is larger than $200$ and smaller than $220$ . Find the progression if its second term is $12$ .

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Solution

Let initial term be a and common difference be d, given $a + d = 12$
and $200 < 9 a + 36 d < 220 ⟹ 200 < 108 - 9 d + 36 d < 220$
$⟹ 92 < 27 d < 112 ⟹ 3.407 < d < 4.148$
$⟹ d = 4$ and the progression is $8, 12, 16, 20, 24, 28, 32, 36, 40, 42, 48, 52$

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All terms of an arithmetic progression are natural numbers. The sum of its nine successive terms, beginning with the first, is larger than 200 and smaller than 220. Find the progression if its second term is 12.

Let initial term be a and common difference be d, given a+d=12 and 200<9a+36d<220⟹200<108−9d+36d<220⟹92<27d<112⟹3.407<d<4.148⟹d=4 and the progression is 8,12,16,20,24,28,32,36,40,42,48,52

All terms of an arithmetic progression are natural numbers. The sum of its nine successive terms, beginning with the first, is larger than $200$ and smaller than $220$ . Find the progression if its second term is $12$ .

Let initial term be a and common difference be d, given $a + d = 12$
and $200 < 9 a + 36 d < 220 ⟹ 200 < 108 - 9 d + 36 d < 220$
$⟹ 92 < 27 d < 112 ⟹ 3.407 < d < 4.148$
$⟹ d = 4$ and the progression is $8, 12, 16, 20, 24, 28, 32, 36, 40, 42, 48, 52$