Question

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

Answer 1

Answer:

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

Step-by-step 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)

• $\dfrac{5}{y-3} +\dfrac{2}{3-y}=$
• $\dfrac{5}{y-3}-\dfrac{2}{y-3}=$
• $\dfrac{5-2}{y-3}=$
• $\dfrac{3}{y-3}$

ii)

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