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Question 82

Sum of all the two-digit numbers that are divisible by 4 is

Solution

Two digit number $$=12,16, 20, 24........96$$

Hence, it is making the AP series $$12+16+20+........96$$

$$n=24-2=22$$

$$d=4$$

$$a=12$$

$$S_n=\dfrac{n(2a+(n-1)d)}{2}$$

Hence, the required sum $$S_n=\dfrac{22(2\times 12+(22-1)\times 4)}{2}$$

$$\Rightarrow S_n=11\times (24+84)$$

$$\Rightarrow S_n=11\times 108$$

$$\Rightarrow S_n=1188$$

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