You will need these formulas:
<--nth term of an A.P.
<--nth term of an G.P.
The first,fifth and seventh term of an Arthimetic Progression(A.P)...
The first term...is 56, the common difference of the A.P IS d
first term of A.P. = = 56
fifth term of A.P. =
seventh term of A.P. =
...the first three consecutive terms of a decreasing Geometric Progression(G.P).
The first term...is 56,...
and the common ratio of the G.P is r
first term of G.P. = = 56
second term of G.P. =
third term of G.P. =
a)(i)Write two equations involving d and r
The first,fifth and seventh term of an Arithmetic Progression(A.P) are
respectively equal to the first three consecutive terms of a decreasing
Geometric Progression(G.P).
(ii)Find the values of d and r
Divide the first equation through by 4 and the second through by 2
Solve the first equation for d
Substitute it in the second equation:
Solve that quadratic for r. [You will get two solutions for r, ignore r=1,
because to have a decreasing G.P., r must be a fraction less than 1.
Substitute to find d
(b) find the sum of the first 10 terms of:
(I) The arithmetic progression
(ii) The geometric progression
You will need these formulas:
<--sum of first n terms of an A.P.
<--sum of first n terms of a G.P.
Now you can do the problem.
If you get stuck, tell me in the thank-you
note form below, and I'll get back to you by email.
Edwin