Q.16. Let f x be a periodic function with period 'p' satisfying
f x + f x + 3 + f x + 6 + . . . . . . + f x + 42 = c o n s tan t   x R , then the sum of digits of 'p' is

Dear Student,
Please find below the solution to the asked query:

A function is peridoci with period with 'p' if Now fx+p=fxDenote constant with kfx+fx+3+fx+6+......+fx+42=k ....iReplace x with x+3fx+3+fx+6+fx+9+......+fx+45=k...iiii-ifx+3+fx+6+fx+9+......+fx+45-fx-fx+3-fx+6+......-fx+42=0Cancelling terms we getfx+45-fx=0fx+45=fxp=45Sum of digits=4+5=9

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