Question about Arithmetic Series: "Molly started her Novemeber Read-a Lot progamme on the first day of the month..."

[I_am_FroM_SOM]

1) Molly started her Novemeber "Read-a Lot" money raising progamme on the first day of the month, at the top of page 63 of her very large book. She read 23 pages the first day, 30 pages the second, then 37 pages on November 3. She continued, reading 7 pages extra each day, until the end of the month. On what page did she finish?

My Work:

November has 30 days.

Nov 1st - 23 pages to read - 1st term
Nov 2nd - 30 pages to read - 2nd term
...
Nov 30th - x pages to read - 30th term

# of #'s/# of terms = 30
Then using the equation for calculating nth term in a sequence we get:
(x - 16)/7 = 30
Or, x - 16 = 210
Or, x = 226
If, nth term/x = 226 then average = (226+23)/2

Therefore, total number of pages Molly has to read = (226+23)/2 x 30
= (226+23)x 15
= 3735 pages to read
Thus, in total Molly will read 3735 pages. If she starts at the top of page 63 or end of page 62 total pages in the book
= (63 - 1) +3735
= 62 + 6735
= 3797

Please, inform me about any mistakes that I have made. Much love and appreciation. ?

 

[Steven G]

Your answer is correct up to the last calculation you made.. Below is how I would do this problem

23 = 16 +1*7
30 = 16 + 2*7
37 = 16 + 3*7
44 = 16 + 4*7
...
? = 16 + 30*7
16*30 +7(1+2+...+30) = 6735
Answer is 62+6735 = 6797

 

[I_am_FroM_SOM]

Sorry I made a typing mistake. By the way I mistyped 6735 instead of 3735 so you answer is also wrong (not to be rude). Unless I have made a mistake again.

 

[Steven G]

The error I was referring to is that (on the last line of your calculations) you wrote 3735 instead of 6735.
What do you claim the answer is?

 

[I_am_FroM_SOM]

I thought it was 3797 as it made sense if all my previous calculations we correct. Please explain if I then have made a mistake in my previous steps.

 

[Dr.Peterson]

I thought it was 3797 as it made sense if all my previous calculations we correct. Please explain if I then have made a mistake in my previous steps.

I agree with your work; as far as I can tell, @Steven G must have copied your mistaken number of 6735 in his work. I don't get 6735 when I follow his work; rather, I get

16*30 +7(1+2+...+30) = 480 + 7(465) = 3735​