Question

Find the 12th term from the end of the AP 4,9,14.....254​

Answer 1

$4 \\ 9 \\ 14 \\ . \\ . \\ . \\ . \\ . \\ . \\ . \\ 254 \\ \\ a = 4 \: \: \: \: \: \: \: \: \: \: \: d = 9 - 4 = 5 \\ \\ tn = 254 \\ \\ \pink{ \huge{tn = a + (n - 1)d}} \\ \\ 254 = 4 + (n - 1)5 \\ \\ 250 = 5n - 5 \\ \\ 255 = 5n \: \: \: \: \: \: \: \: \\ \\ \frac{255}{5} = n \\ \\ 51 = n \\ \\ hence \: \: \: \: total \: \: \: 51 \: \: \: terms \: \: \\ are \: \: \: there \\ \\ hence \: \: \: \: last \: \: \: 10th \: \: \: \\ term \: \: \: will \: \: \: be \\ \\ \pink{t42} \\ \\ \blue{hence} \\ \\ t42 = 4 + (42 - 1)5 \\ \\ = 4 + 41 \times 5 \\ \\ = 4 + 205 \: \: \: \: \: \: \\ \\ = 209 \: \: \: \: \: \: \: \: \: \: \: \: \: \:$