let's firstly convert the mixed fractions to improper fractions and then get their difference.
![\stackrel{mixed}{8\frac{7}{8}}\implies \cfrac{8\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{71}{8}} ~\hfill \stackrel{mixed}{6\frac{3}{4}}\implies \cfrac{6\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{27}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{71}{8}-\cfrac{27}{4}\implies \cfrac{1(71)~~ -~~2(27)}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{71-54}{8}\implies \cfrac{17}{8}\implies 2\frac{1}{8}](https://tex.z-dn.net/?f=%5Cstackrel%7Bmixed%7D%7B8%5Cfrac%7B7%7D%7B8%7D%7D%5Cimplies%20%5Ccfrac%7B8%5Ccdot%208%2B7%7D%7B8%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B71%7D%7B8%7D%7D%20~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B6%5Cfrac%7B3%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B6%5Ccdot%204%2B3%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B27%7D%7B4%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B71%7D%7B8%7D-%5Ccfrac%7B27%7D%7B4%7D%5Cimplies%20%5Ccfrac%7B1%2871%29~~%20-~~2%2827%29%7D%7B%5Cunderset%7B%5Ctextit%7Busing%20this%20LCD%7D%7D%7B8%7D%7D%5Cimplies%20%5Ccfrac%7B71-54%7D%7B8%7D%5Cimplies%20%5Ccfrac%7B17%7D%7B8%7D%5Cimplies%202%5Cfrac%7B1%7D%7B8%7D)
Answer:
A
Step-by-step explanation:
The sequence of positive odd numbers is
1, 3, 5, 7, ......
This is an arithmetic sequence with common difference d
d = 3 - 1 = 5 - 3 = 7 - 5 = 2
The sum to n terms of an arithmetic sequence is
=
[2a + (n - 1)d ]
where a is the first term
here a = 1, d = 2, n = 12, hence
=
[1 + (11 × 2) ]
= 6 [ 2 + (11 × 2) ]
= 6 × 24 = 144 → A