Answer:
See below.
Step-by-step explanation:
I will assume that 3n is the last term.
First let n = k, then:
Sum ( k terms) = 7k^2 + 3k
Now, the sum of k+1 terms = 7k^2 + 3k + (k+1) th term
= 7k^2 + 3k + 14(k + 1) - 4
= 7k^2 + 17k + 10
Now 7(k + 1)^2 = 7k^2 +14 k + 7 so
7k^2 + 17k + 10
= 7(k + 1)^2 + 3k + 3
= 7(k + 1)^2 + 3(k + 1)
Which is the formula for the Sum of k terms with the k replaced by k + 1.
Therefore we can say if the sum formula is true for k terms then it is also true for (k + 1) terms.
But the formula is true for 1 term because 7(1)^2 + 3(1) = 10 .
So it must also be true for all subsequent( 2,3 etc) terms.
This completes the proof.
Y = -14 i believe this is the correct answer
Answer:
4376
Step-by-step explanation:
8, −24, 72, -216, 648, -1944, 5832
Multiply the next number by -3
8 x -3 = -24
-24 x -3 = 72
72 x -3 = -216
-216 x -3 = 648
648 x -3 = -1944
-1944 x -3 = 5832
adding all 7 numbers
8 + (−24)+72 + (-216)+648+ (-1944)+5832 = 4376
Answer:
v ≈ 113.09
Step-by-step explanation:
v = πr^2*h
v = π*2^2*9
v = π*4*9
v = π*36
v = 113.097335529
hope this helps :)
Answer:
f(50) = 31928.24 thousands
Therefore, it means that the US population in year 1850 is 31928.24 thousands
Step-by-step explanation:
Given the function;
f(x)=165.6x^1.345
Where;
f(x) is in thousand and
x is the number of year after 1800
To determine f(50), we will substitute x = 50 into the function of f(x);
f(50)=165.6(50)^1.345
f(50) = 31928.24 thousands
Since f(50) is the US population in year 1800+50 = 1850
Therefore, the US population in year 1850 is 31928.24 thousands
