Question 133619
Not sure what A.P means. But for the series in number 1, each successive number is 7 less than the previous number. So, if you divide {{{500/7}}}, you get the number of items in the series that are greater than 0. {{{500/7}}} = 71. take {{{71*7}}} and get 497. The last positive term would be {{{500-(71*7)}}} = 3.

Likewise for problem 2, each item in 1.5 greater than the previous item. So {{{54/(1.5)}}} = 36. The 36th entry is {{{-54 + (36*1.5) }}} = 0. Since 0 is neither positive or negative, take one more step of 1.5. 
Answer is 36+1 = 37 steps