ed saved 50 $ one week. For the next 6 weeks he saved 25$ more than he saved the week before. How much did he save in all?

Question

Another student answered the question saying 50$ + 6(25$) = 200$ What was the error?

Answer 1

1st week=$50

2nd week=$75

3rd week=$100

4th week=$125

5th week=$150

6th week=$175

7th week=$$200

add the amounts of money to get $875 that he saved in all

this is an arithmetic progression

sum of n terms=(n/2)[2a+(n-1)d] where a is the first term and d is the difference between terms

                      =(7/2)[2*50+(7-1)25]

                      =(7/2)[100+6*25]

                      =(7/2)[100+150]

                      =(7/2)[250]

                      =7*125

                      =$875

Answer 2

Ed saved $50 in one week.

Every week after for 6 weeks, he earns $25 more than the week one which means he saved $75 on those weeks.

 

Week 1 : $50

Week 2 - 7 : $75

 

Answer: $50 + 6*($75) = $50 + $450 = $500.

Ed saves $500 in all.

 

OR

 

Ed saved $50 in week 1, and if he saves $25 more than the previous week, that means:

 

Week 1: $50

Week 2: $75

Week 3: $100

Week 4: $125

Week 5: $150

Week 6: $175

Week 7: $200

 

Note that the savings between each week increased by $25. Then find the total which is $875.