Makya was conducting a physics experiment. He rolled a ball down a ramp and calculated the distance covered by the ball at different times. The ball rolled a distance of 1 foot during the first second, 3 feet during the next second, and so on. If the distances the ball rolled down the ramp each second form an arithmetic sequence, determine the distance the ball rolled down during the fifteenth second.

Answer:  Makya was conducting a physics experiment. At 15th second, distance rolled will be 29 feet. Solution: Given that Makya is conducting physics experiments. He rolled a ball down a ramp and calculated the distance covered by the ball at different time. Ball rolled a distance of 1 foot during first second. Ball rolled a distance of 3 feet during second second. Given that distance rolled with the time formed an arithmetic sequence. [tex]\text { Which means } a_{1}=1, a_{2}=3 \ldots \ldots[/tex]We need to calculate distance rolled at 15th second that is 15th term of Arithmetic sequence when,[tex]\mathrm{a}_{1}=1, \mathrm{a}_{2}=3 \text { and common difference } \mathrm{d}=\mathrm{a}_{2}-\mathrm{a}_{1}=3-1=2[/tex][tex]\text { Formula of } \mathrm{n}^{\text {th }} \text { term is } \mathrm{a}_{\mathrm{n}}=\mathrm{a}_{1}+(\mathrm{n}-1) \mathrm{d}[/tex][tex]\text { So when } \mathrm{n}=15, \mathrm{a}_{15}=1+(15-1) 2=1+14 \times 2=29[/tex]Hence at 15th second, distance rolled will be 29 feet.