Find the sum of all three digit numbers each of which leaves the remainder 2 when divided by 3

Find the sum of all three digit numbers each of which leaves the remai

1.	Find the sum of all three digit numbers each of which leaves the remainder 2 when divided by 3
Answer» Three digit number which leaves remainder\xa02\xa0when divided by\xa05\xa0is102,107,112,117......997This form an AP whose first term is\xa0=102,\xa0d=5Let\xa0997\xa0is the n th term of AP i.e.\xa0an\u200b=997an\u200b=a+(n−1)d997=102+(n−1)55n=900n=180Sum of all three digits which leaves remainder\xa02\xa0when divided by\xa05\xa0isSn\u200b=n/2 \u200b[2a+(n−1)d]=180/2 \u200b[2×102(180−1)5]=90[204+179×5]=90[204+895]=90×1099=98910