Answer:
7 terms
Step-by-step explanation:
There is a common ratio between consecutive terms, that is
r = 10 ÷ 2 = 50 ÷ 10 = 5
This indicates the sequence is geometric with nth term
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 2 and r = 5, then equating to 31250 and solving for n
2 × [tex]5^{n-1}[/tex] = 31250 ( divide both sides by 2 )
[tex]5^{n-1}[/tex] = 15625 = [tex]5^{6}[/tex]
Since bases on both sides are equal, both 5, equate exponents
n - 1 = 6 ( add 1 to both sides )
n = 7
That is there are 7 terms in the sequence
