\[\text { The } 20^{\text {th }} \text { term from the end of the progression } 20,19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \ldots,-129 \frac{1}{4} \text { is : }\]
Solutions · 1
Official solution
\[20,19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \ldots \ldots,-129 \frac{1}{4}\]
This is A.P. with common difference
\[d1=−1+41=−43−12941,…………...1941,20\]
This is also A.P. \[\mathrm{a}=-129 \frac{1}{4}\] and \[\mathrm{d}=\frac{3}{4}\]
Required term =
\[−12941+(20−1)(43)=−129−41+15−43=−115\]