The first one is 180 because the angles of a triangle add up to 180
angles 1 and 4
And finally, the last one is 1
Firstly, we have to find the mean. The mean is simply the average of the numbers, which we find by adding each number in the sequence and then dividing that result by the total amount of numbers.
<em>13.3 + 14.3 + 15.3 + 16.3 + 17.3 = 76.5</em>
<em>76.5 / 5 = 15.3
</em>Okay, so our average is 15.3.
<em>
Now, </em>we have to subtract the mean from each number and then square the result.
<em>(13.3 - 15.3)^2 = 4</em>
<em>(14.3 - 15.3)^2 = 1</em>
<em>(15.3 - 15.3)^2 = 0</em>
<em>(16.3 - 15.3)^2 = 1</em>
<em>(17.3 - 15.3)^2 = 4
</em>Now we have to find the mean of those numbers!
<em>
4 + 1 + 0 + 1 + 4 = 10
10 / 2 = 2
</em>Finally, we take the square root of that number and we have our standard deviation. =)<em>
</em>
Answer:
The explicit rule of the geometric sequence
aₙ = 187.5 (0.8)ⁿ⁻¹
Step-by-step explanation:
<u><em> Step(i):-</em></u>
Given that the third term of the sequence = 120
tₙ = a rⁿ⁻¹
t₃ = a r³⁻¹ = ar²
120 = ar² ..(i)
Given that the fifth term of the given geometric sequence = 76.8
tₙ = a rⁿ⁻¹
t₅ = a r⁵⁻¹ = a r⁴
76.8 = a r⁴...(ii)
<u><em>Step(ii):</em></u>-
Dividing (ii) and (i)
r² = 0.64
r =√ 0.64 = 0.8
Substitute r= 0.8 in equation (i)
120 = ar²
120 = a(0.8)²
⇒ 
<u><em>Step(iii):-</em></u>
The explicit rule of the geometric sequence
aₙ = a rⁿ⁻¹
put a= 187.5 and r = 0.8
aₙ = 187.5 (0.8)ⁿ⁻¹
