Question

Answer both Question 11 and 12. I will make Brainelist + 50 points ​

Answer 1

• #11. i) 5, ii) 6, iii) - 4, iv) 6
• #12- see below

Explanation:

#11

Given equation for sum of the first n terms

• 
  `S_n=7n-2n^2`

Using the equation solve the following

i)

The first term
`t_1`, is same as the sum of the first 1 term, so n = 1

• 
  `t_1=S_1=7(1)-2(1)^2=7-2=5`

ii)

Sum of the first 2 terms, when n = 2

• 
  `S_2=7(2)-2(2)^2=14-8=6`

iii)

Common difference is the difference between two consequitive terms.

First, find the second term:

• 
  `t_2=S_2-t_1=6-5=1`

Now find the difference between the first two terms:

• 
  `d=t_2-t_1=1-5=-4`

iv)

We need to find such n that
`S_n` = - 30

• 
  `7n - 2n^2=-30`
• 
  `2n^2 - 7n-30=0`
• 
  `2n^2-12n+5n-30=0`
• 
  `2n(n-6)+5(n-6)=0`
• 
  `(n-6)(2n+5)=0`
• 
  `n=6` is the only positive root

So the answer is 6

#12

Simplifying in steps as below

a) i)

• 
  `(5)/(y-3) +(2)/(3-y)=`
• 
  `(5)/(y-3)-(2)/(y-3)=`
• 
  `(5-2)/(y-3)=`
• 
  `(3)/(y-3)`

ii)

• 
  `\cfrac{1}{m+3} +\cfrac{2m}{m^2-9} =`
• 
  `\cfrac{1}{m+3} +\cfrac{2m}{(m-3)(m+3)} =`
• 
  `\cfrac{m-3}{(m-3)(m+3)}+\cfrac{2m}{(m-3)(m+3)} =`
• 
  `\cfrac{m-3+2m}{(m-3)(m+3)} =`
• 
  `\cfrac{3m-3}{(m-3)(m+3)}`