A nail is 3cm long and is driven into wood by blows of a hammer. The first blow drives it in 1.25cm and each successive blow drives it in by 3/5 of the previous distance except the last for which the distance is less. Find how many blows mush be used​

four blows of hammer

Step-by-step explanation:

The first blow of hammer drove the 3cm nail into wood by 1.25cm leaving 1.75cm of the nail

3/5 or 0.6cm of the nail was also driven into wood by the second blow of hammer leaving 0.7cm of the nail

The third is also drove 0.6cm of the nail in leaving 0.1cm

since 0.1cm is not up to 0.7cm,it will definitely be driven in completely by the fourth blow of hammer.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

answer: an 8-foot rope is tied from the top of a pole to a

stake in the ground, as shown in the diagram

below

step-by-step explanation: