Hence, the sum of the given GP is 16347
<h2>What is a series?</h2>
a series is the cumulative sum of a given sequence of terms. Typically, these terms are real or complex numbers, but much more generality is possible.
<h3>How to solve?</h3>
we can identify from the given geomertric series.
first term = a(say) = 3
geometric factor of progression = r(say) = 4
Sum of the first 7 terms = a(
) ,where n is 7
Sum = 3(
) = 16348-1
= 16347
Hence, the sum of the given GP is 16347.
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Answer:
Step-by-step explanation:
a1=2/3
sequence is 2/3,3/4,4/5,...
for numerator a1=2
d=3-2=1
numerator of nth term=a1+(n-1)d=2+(n-1)×1=2+n-1=n+1
denominator = 1 more than numerator=n+1+1=n+2
so an=(n+1)/(n+2)
or for denominator a1=3,d=4-3=1
denominator of nth term=3+(n-1)×1=3+n-1=n+2
an=(n+1)/(n+2)
Answer:
698 fishes
Step-by-step explanation:
Generally, we can represent an exponential growth function as;
y = a•(1 + r)^t
originally, there were 3 fishes
The original value in this case means a = 3
After 6 weeks, there were 31
31 in this case is y
r is the increase percentage or rate
t is the time
So, we have it that;
31 = 3•(1 + r)^6
31/3 = (1 + r)^6
10.33 = (1 + r)^6
ln 10.33 = 6 ln (1 + r)
ln 10.33/6 = ln (1 + r)
e^0.3892 = (1 + r)
1 + r = 1.476
r = 1.476-1
r = 0.476 or 47.6%
So the growth percentage or rate is 47.6%
For 14 weeks, we simply have the value of t as 14;
So ;
y = 3•(1 + 0.476)^14
y = 3(1.476)^14
y = 698 fishes
Answer:
41
Step-by-step explanation:
an = a1 + (n-1)d
a_n = the nᵗʰ term in the sequence = 10
a_1 = the first term in the sequence = 5
d = the common difference between terms = 4
a10 = 5 + (10-1)4
a10 = 5 + (9)4
a10 = 5 + 36
a10 = 41
Answer:
19.2
Step-by-step explanation:
Add 12 squared to 15 squared(144+225)
Square root the answer(
)
Round to the nearest tenth(19.209)
