Product of 4 consecutive numbers in GP is 256.
Answers
Answered by
3
256,256,256,256
as ×1 common multiplecation
as ×1 common multiplecation
Answered by
2
Suppose the first four consecutive terms of G.P are a,ar,ar2, ar3 where a is the first term and r is the common ratio.
Now common ratio = r = 4
And product of first four consecutive terms is 256, so we have;
a×ar×ar2×ar3 = 256⇒ a×4a×a42×a43 = 256⇒ a4×4096 = 256⇒a4 = 2564096⇒a4 =116⇒a4 = 124Comparing both sides of the equation we get;a = 12
So third term = ar2 = 12×42 = 8
Therefore 3rd term of G.P. is 8.
Now common ratio = r = 4
And product of first four consecutive terms is 256, so we have;
a×ar×ar2×ar3 = 256⇒ a×4a×a42×a43 = 256⇒ a4×4096 = 256⇒a4 = 2564096⇒a4 =116⇒a4 = 124Comparing both sides of the equation we get;a = 12
So third term = ar2 = 12×42 = 8
Therefore 3rd term of G.P. is 8.
Similar questions