an ap has 37 terms sum of middle three are 225 and last three is 428 find ap
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Given:
T(18)+T(19)+T(20)=225=>
T(1)+18d=75-------(1)
T(35)+T(36)+T(37)=429=>
T(1)+35d=143-----(2)
solving the system of (1) & (2) for
T(1) & d, get
T(1)=3
d=4
=> the A.P. is
3, 7, 11,....,(4n-1),...
or
3+7+11+...+(4n-1)+...
where n=1,2,3,...