The number series below is made by writing the same group of numbers again and again.
4 1 4 6 1 4 9 4 1 4 6 1 4 9 4 1 4
If the series is continued in the same way, how many times will 4 appear in the first 80 terms?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 35
Count the number in one full group, multiply by the number of full groups, then add the terms of the part-group at the end.
The series starts again with 4 1 4 after the 7th term, so the repeating group is 4 1 4 6 1 4 9 (7 numbers); it has three 4’s
\(80 \div 7\) gives 11 full groups (77 terms) and 3 terms more
4’s in 11 full groups \(=11\times3=33\)
The 3 extra terms are 4 1 4, which have two 4’s
Total \(=33+2=35\)