Concept 10 of 19Foundation
Watch on YouTubeVideoCounting terms & reverse problems
Three classic reverse questions:
Q1. How many terms in 3, 6, 9, …, 99?
Count formula: n = (last − first)/d + 1 = (99 − 3)/3 + 1 = 33.
Q2. Which term of 3, 7, 11, … equals 99?
aₙ = 3 + (n−1)·4 = 4n − 1 = 99 → n = 25 (25th term).
Q3. Smallest n such that 1+2+…+n > 100?
Try n(n+1)/2: n=13 → 91 (no), n=14 → 105 (yes). n = 14.
Same approach for "how many multiples of 5 between 1 and 200?" — use the count formula.
Example
How many multiples of 7 between 1 and 100?
First multiple 7, last 98. n = (98−7)/7 + 1 = 14.
First multiple 7, last 98. n = (98−7)/7 + 1 = 14.
💡 Tip:Count formula (last − first)/d + 1 works for ANY arithmetic-style counting.
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5 questions to check what you just read.
0 / 5
- Q1.How many multiples of 5 between 1 and 50 (inclusive)?
- Q2.Number of terms in 2, 5, 8, …, 50?
- Q3.Which term of 7, 11, 15, 19, … is 87?
- Q4.Smallest n such that 1 + 2 + … + n > 50?
- Q5.How many 3-digit numbers are divisible by 10?