Concept 5.4
Is It a Term?
Source: NCERT Mathematics, Class 1010 minute lesson
Formal statement
To check whether a number x is a term of an AP, solve a + (n − 1)d = x for n. The number is a term only if n is a positive whole number.
The intuition
The formula always hands you some value of n. The real question is whether that value is a position. Positions are 1, 2, 3, …, so a fraction means the AP steps over the number.
NCERT asks whether 301 is a term of 5, 11, 17, 23, …. Solving gives n − 1 = 296/6, which is not a whole number. So 301 is never reached.
The attention
Look at what kind of number n turns out to be.
301 = 5 + (n − 1) × 6 → n = 50.33…
Look hereNot here
- Look here
- The value of n. A position must be a whole number: 1, 2, 3, … There is no 50.33rd term.
- Not here
- The number being tested. 301 is bigger than the first few terms, so it looks reachable. Size never decides it. Only n does.
- What it teaches
- Checking what kind of answer you got is part of solving, not an extra step.