## Sequence (A, B, C, D) | (A,B,C) in AP, (B,C,D) in GP

$D - A$   ……….   $( \,A, \; B, \; C, \; D \,)$

$10$   ……….   $( \,6, 9, 12, 16 \,) \; = \; ( \,6, 3^2, 12, 4^2 \,)$

$28$   ……….   $( \,8, 16, 24, 36 \,) \; = \; ( \,8, 4^2, 24, 6^2 \,)$
$28$   ……….   $( \,72, 81, 90, 100 \,) \; = \; ( \,72, 9^2, 90, 10^2 \,)$

$45$   ……….   $( \,4, 16, 28, 49 \,) \; = \; ( \,4, 4^2, 28, 7^2 \,)$

$55$   ……….   $( \,306, 324, 342, 361 \,) \; = \; ( \,306, 18^2, 342, 19^2 \,)$

$91$   ……….   $( \,870, 900, 930, 961 \,) \; = \; ( \,870, 30^2, 930, 31^2 \,)$

$136$   ……….   $( \,60, 100, 140, 196 \,) \; = \; ( \,60, 10^2, 140, 14^2 \,)$
$136$   ……….   $( \,440, 484, 528, 576 \,) \; = \; ( \,440, 22^2, 528, 24^2 \,)$
$136$   ……….   $( \,1980, 2025, 2070, 2116 \,) \; = \; ( \,1980, 45^2, 2070, 46^2 \,)$

$153$   ……….   $( \,208, 256, 304, 361 \,) \; = \; ( \,208, 16^2, 304, 19^2 \,)$

$171$   ……….   $( \,270, 324, 378, 441 \,) \; = \; ( \,270, 18^2, 378, 21^2 \,)$

$190$   ……….   $( \,66, 121, 176, 256 \,) \; = \; ( \,66, 11^2, 176, 16^2 \,)$
$190$   ……….   $( \,899, 961, 1023, 1089 \,) \; = \; ( \,899, 31^2, 1023, 33^2 \,)$
$190$   ……….   $( \,3906, 3969, 4032, 4096 \,) \; = \; ( \,3906, 63^2, 4032, 64^2 \,)$

$253$   ……….   $( \,6972, 7056, 7140, 7225 \,) \; = \; ( \,6972, 84^2, 7140, 85^2 \,)$

$325$   ……….   $( \,300, 400, 500, 625 \,) \; = \; ( \,300, 20^2, 500, 25^2 \,)$
$325$   ……….   $(11556, 11664, 11772, 11881) \; = \; (11556, 108^2, 11772, 109^2 \,)$

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## About benvitalis

math grad - Interest: Number theory
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