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Mathematics · Arithmetic Progressions · NCERT Examples

Example 7

A complete, independently verified solution for NCERT Example 7.

Mathematics · Chapter 5 · NCERT Examples

Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.

NCERT Example

Example 7

How many two-digit numbers are divisible by 3?

Solution

Board-exam working:

an=a+(n1)da_n=a+(n-1)d

The first two-digit multiple of 3 is 12 and the last is 99, so the AP is 12,15,…,99 with a=12,d=3,l=99.

Use l=a+(n−1)d: 99=12+3(n−1).

Thus 87=3(n−1), n−1=29 and n=30.

Check: a₃₀=12+29×3=12+87=99.

Final answer

30 numbers.