THE SUM OF THE FIRST TWO TERM OF A GP IS 6 AND THE SUM OF THE 5TH AND 8TH TERM IS 288. SOLVE
2 answers
If you're going to promote a Greater TOMORROW, please learn to spell it correctly.
a+ar = 6
ar^4 + ar^7 = 288
a(1+r) = 6
ar^4(1+r^3) = 288
1+r^3 = (1+r)(1-r+r^2), so
r^4 * a(1+r)(1-r+r^2) = 288
6r^4(1-r+r^2) = 288
r^4(1-r+r^2) = 48
We probably want r an integer, so try to see what factors we have of 48
48 = 1*48
48 = 16*3 - bingo
r = 2
so, a = 2
The sequence is
2,4,8,16,32,64,128,256
a1+a2 = 2+4 = 6
a5+a8 = 32+256 = 288
ar^4 + ar^7 = 288
a(1+r) = 6
ar^4(1+r^3) = 288
1+r^3 = (1+r)(1-r+r^2), so
r^4 * a(1+r)(1-r+r^2) = 288
6r^4(1-r+r^2) = 288
r^4(1-r+r^2) = 48
We probably want r an integer, so try to see what factors we have of 48
48 = 1*48
48 = 16*3 - bingo
r = 2
so, a = 2
The sequence is
2,4,8,16,32,64,128,256
a1+a2 = 2+4 = 6
a5+a8 = 32+256 = 288
1 answer