Determine whether 97 and 172 are terms of the sequence $t_n = 5n - 3$ for $n \geq 1$.                              [Page No. 179]

For 97: $5n - 3 = 97$

$$\Rightarrow \quad 5n = 100$$

$$\Rightarrow \quad n = 20$$

So, $97$ is a term (the $20^{th}$ term).

For 172: $5n - 3 = 172$

$$\Rightarrow \quad 5n = 175$$

$$\Rightarrow \quad n = 35$$

So, $172$ is a term (the $35^{\mathrm{th}}$ term).

Caution
Students should make sure that the value of $n$ comes out to be a positive whole number while checking whether a given number is a term of a sequence. A fractional $n$ means the number is not a term.