Question

Write the expression $a_n-a_k$ for the A.P. $a,a+d,a+2d,.....$ .
Hence, find the common difference of the A.P. for which ${11}^{th}$ term is $5$ and ${13}^{th}$ term is $79$.

Answer 1

Formula,

$a_n=a+(n-1)d$

$a_k=a+(k-1)d$

$a_n-a_k=a+(n-1)d-a-(k-1)d$

$=a+nd-d-a-kd+d$

$\therefore a_n-a_k=(n-k)d$

Given,

$a_{11}=a+10d=5$.......(1)

$a_{13}=a+12d=79$........(2)

solving (1) and (2), we get,

$2d=74$

$\therefore d=37$