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Question
How many two-digit number are divisible by 6?
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Solution
The two digit numbers divisible by 6 are 12, 18, 24,……, 96
Clearly, these number are in AP.
Here, a = 12 and d = 18 - 12 = 6
Let this AP contains n terms. Then,
an = 96
⇒ 12 + (n-1) × 6 = 96 [ an = a +(n-1) d]
⇒ 6n + 6 = 96
⇒ 6n = 96 - 6 =90
⇒ n= 15
Hence, these are 15 two-digit numbers divisible by 6.
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