Bhaskara II Acharya/Lilavati/Chapter V/124

: : Chapter $\text {V}$: Progressions: $124$

 * ''In an expedition to seize his enemy's elephants, a king marched $2$ yojanas on the first day.
 * Say, intelligent calculator, with what increasing rate of daily march did he proceed, since he reached his foe's city, a distance of $80$ yojanas, in a week?

Solution
His march was increased by the rate of $\dfrac {22} 7$ yojanas per day.

Proof
We are given that the daily rate of march increases each day by an arithmetic sequence.

Let the initial term be denoted by $a_0$.

Let the common difference, which we are to find, be denoted by $d$.

Let the number of days march be $n$.

Let the total number of yojanas marched be $T$.

Then: