Question

Insert $5$ arithmetic means between $3$ and $33$.

Answer 1

We are here inserting 5 arithmetic means between 3 and 33. So the total number of terms are 7.

$a_1=3a_7=33n=7d=?$

$a_n=a+(n-1)d{a}_7=3+(7-1)d$

$33=3+6d6d=30d=5$

$\therefore AP3,8,13,18,23,28,\mathrm{33.....}$