Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Mathematics

Grade10

Easy

Question

The explicit formula for the sequence 360, 180, 90, 45 … is __________

$a_{n} = {(\frac{1}{2})}^{n - 1}$
$a_{n} = 360 \times {(\frac{1}{2})}^{n - 1}$
$a_{n} = 45 \times {(2)}^{3}$
$a_{n} = \frac{1}{2} \times {(360)}^{n - 1}$

hint Hint:

In this question, we have to find the explicit formula for the sequence 360, 180, 90, 45 … As the explicit formula for GP is $a subscript n end subscript equals a subscript 1 end subscript cross times open parentheses r close parentheses to the power of n minus 1 end exponent$ , where a is the first term, r is the constant ratio of the geometric sequence and n is the number of terms. So, by putting the available information, we can find the required explicit formula.

The correct answer is: $a subscript n end subscript equals 360 cross times open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of n minus 1 end exponent$

The explicit formula for a geometric sequence is $a subscript n end subscript equals a subscript 1 end subscript cross times open parentheses r close parentheses to the power of n minus 1 end exponent$
First term, a = 360
The constant ratio of the geometric sequence, r = $fraction numerator 180 over denominator 360 end fraction equals fraction numerator 1 over denominator 2 end fraction$
So, the explicit formula for the given sequence is $a subscript n end subscript equals 360 cross times open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of n minus 1 end exponent$

Related Questions to study

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.