CIE Pure Mathematics Paper 1 Doubt

[Dania]

I need HELP, please!

How do I show that the mid-points of 2 3D vectors coincide?

Also,

(a) The fifth term of an arithmetic progression is three times the second term, and the third term is 10.
Find (i) the first term, (ii) the common difference, (iii) the 20th term.

(b) The nth term, t(n), of a sequence is given by - t(n) = p + nq, where p and q are constants.

(i) Write down, in terms of p and q, the 6th term of the sequence.
(ii) Find, in terms of p and q, the sum of the first six terms.

[S.M.A.T]

a)i)
2nd term=a+d
 5th term=a+4d

a+4d=3×(a+d)
d=2a

a+2d=10
a+(2×(2a))=10
5a=10
a=2

ii)d=2×2=4
iii)20th term=2+(19×4)=78

b)i)t(6)=p+6q
    
   ii)sum=(n/2)×(L+a),where L is last term
           =(6/2)×(p+6q+p+q)
           =3×(2p+7q)
           =6p+21q
  

[Dania]

Thank You

[Dania]

By the way, would you happen to know how I would show that that 2 vectors coincide?

[S.M.A.T]

By the way, would you happen to know how I would show that that 2 vectors coincide?

here
See post number 378&379

If you have problem please tell me

[astarmathsandphysics]

I did a page on my website. Will post a link when I get home.

[astarmathsandphysics]

How to find the point of intersection of two lines.

http://astarmathsandphysics.com/a_level_maths_notes/C4/a_level_maths_notes_c4_finding_the_point_of_intersection_of_two_lines_in_three_dimensions.html