Question

PLEASE HELP WITH EXPLANATION! 15 POINTS!

Answer 1

$\bf a_n=2\cdot a_{n-1}$  is just a notation way to say, "the nth term will be found by multiplying 2 times the term right before"

so, if you want to find the 27th term, just see what the 26th term is, 2 * "26th term value" and that's the 27th term

$a_1$ simply means, the first term in the geometric sequence

is a geometric sequnce, because is "multiplying something" to get to the next term, if it were adding something, it'd be an arithmetic sequence

so, we know the first term is 4, and the multiplier or "common ratio" is 2
is given in the $a_n=$ part

thus    $\bf \begin{array}{crllll} term&value\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ a_1&4\\ a_2&2\cdot 4\\ a_3&2\cdot 2\cdot 4\\ a_4&2\cdot 2\cdot 2\cdot 4\\ a_5&2\cdot 2\cdot 2\cdot 2\cdot 4\\ a_6&2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 4 \end{array}$