Question

Find the ${10}^{th}$ term from the end of the $A.P.4,9,14,....,254$.

Answer 1

Given AP: $4,9,14,....,254$

$a_2=9,a_1=4$ Common difference $=a_2-a_1=9-4=5$

$r^{th}$ term from end $=(n-r+1{)}^{th}$ term from starting

Given $a_n=254$

$n^{th}$ term of an AP $a_n=a_1+(n-1)d$

$254=4+(n-1)5250=(n-1)550=n-1n=51$

${10}^{th}$ term from end $=(51-10+1{)}^{th}$ term from starting $=42^{nd} term from starting

$a_n=a_1+(n-1)d{a}_{42}=4+41\times 5=4+205=209$