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

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Answer 1 · 2016-01-05T15:46:24

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

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

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

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

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

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

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