An important question from ML Agarwal of Class10 for board examination. How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?
ML Agarwal (avichal publication) arithmetic progression chapter 9 question no 20(ii)
Rajan@2021Guru
How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?
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The number lies between 10 to 300, which when divided by 4 leaves the remainder 3 are 11,15,19,...299. Clearly, it is an AP with first term a=11, common difference d=4 and last term l=299.
Let the are n terms in the given AP.
Then, an=299
a+(n−1)d=299
11+(n−1)4=299⇒n−1=72⇒n=73
Hence, there are 73 such terms.