The sum of the first three terms of an arithmetic progression is 42 and the product of the first and third term is 52 . find the first term and the common difference .
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let the first three terms be a-d, a, a+d.
ATQ
a-d + a+ a+d =42
3a=42
a=42/3
=> a=14
now,
(a-d)(a+d)=52
=>(a)2-(d)2 =52
=>(14)2-(d)2=52
=>196-52=(d)2
=>144=(d)2
=>d=12
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