Question

Write the expression $a_n-a_k$ for the $A.P.$ $a,a+d,a+2d,..$${11}^{th}$ term is $5$ and ${13}^{th}$ term is $79$$a_{10}-a_5=200$${20}^{th}$ term is $10$ more than the ${18}^{th}$ term.

Answer 1

$a,a+d,a+2d,........$

${11}^{th}$ term is $5$

$t_{11}=a+(11-1)d=\mathrm{5..........}\left(1\right)$

$=>a+10d=5$

$t_{13}=a+12d=79..............\left(2\right)$

$=>t_{20}=a+19d=a+17d+10$

$=>2d=10$

$=>d=5$

$=>a+(10\times 5)=5$

$=>a=-45$

$a,a+d,a+2d,..............$

$-45,-40,-35,30,............$