Whats the missing term in the geometric sequence 1, __, 49?

1 Answer
Jan 5, 2016

Answer:

#2^("nd") " term " ->7#

#color(blue)("Have a look at the way the sequence is built!")#

Explanation:

As I understand it, a Geometric sequence is of structure:

#ar^0, ar^1, ar^2, ar^3......# where r is the Geometric Ratio

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Note that "r^0 = 1color(white)(...)" so "ar^0 = a#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In your case the first term #-> ar^0 =1# so #a=1#

Given that the third term #-> ar^2=49#
as #a=1 " then "1 xx r^2 =49#

So #sqrt(r^2)=r = sqrt(49) = 7#

The missing term #-> ar^1 = 1 xx 7^1#

#7^1 = 7 color(white)(...)#so the missing term is 7