Answer:
a = 36, b = 54
Step-by-step explanation:
Since the terms are in arithmetic progression then there is a common difference d between consecutive terms , that is
b - a = 72 - b ( add b to both sides )
2b - a = 72 → (1)
and
a + b - 72 = b - a ( subtract b - a from both sides )
2a - 72 = 0 ( add 72 to both sides )
2a = 72 ( divide both sides by 2 )
a = 36
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Substitute a = 36 into (1) and evaluate for b
2b - 36 = 72 ( add 36 to both sides )
2b = 108 ( divide both sides by 2 )
b = 54
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Thus a = 36 and b = 54
The sequence is therefore 36, 54, 72, 90 , .....
