Question

Wang Lei and Amira were asked to find an explicit formula for the sequence 30\,,\,150\,,\,750\,,\,3750,...30,150,750,3750,...30, comma, 150, comma, 750, comma, 3750, comma, point, point, point.
Wang Lei said the formula is g(n)=30\cdot5^{\large{n-1}}g(n)=30⋅5

n−1

g, left parenthesis, n, right parenthesis, equals, 30, dot, 5, start superscript, n, minus, 1, end superscript, and

Amira said the formula is g(n)=6\cdot5^{\large{n}}g(n)=6⋅5

n

g, left parenthesis, n, right parenthesis, equals, 6, dot, 5, start superscript, n, end superscript.

Which one of them is right?

Answer 1

Answer:

Wang Lei is right.

Step-by-step explanation:

Given sequence,

30, 150, 750, 3750,...

Since,

$\frac{150}{30}=\frac{750}{150}=\frac{3750}{750}......= 5$

Thus, 30, 150, 750, 3750,... is a geometric sequence.

We know that,

The explicit formula of a geometric sequence is,

$g(n)=a r^{n-1}$

Where,

a = first term,

r = common ratio,

Here, a = 30, r = 5,

Thus, the required explicit formula,

$g(n) = 30 (5)^{n-1}$

Hence, Wang Lei is right.