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.
125.13
Step-by-step explanation:
ndex Notation and Powers of 10
10 to the Power 2
The exponent (or index or power) of a number says
how many times to use the number in a multiplication.
102 means 10 × 10 = 100
(It says 10 is used 2 times in the multiplication)
Example: 103 = 10 × 10 × 10 = 1,000
In words: 103 could be called "10 to the third power", "10 to the power 3" or simply "10 cubed"
Example: 104 = 10 × 10 × 10 × 10 = 10,000
In words: 104 could be called "10 to the fourth power", "10 to the power 4" or "10 to the 4"
Answer:
X=8
Step-by-step explanation:
Answer:
$46,141.71
Step-by-step explanation:
This looks about right, based on weekly deposits for the duration. However, I cannot vouch for it entirely, as the number of weekly deposits in 15 years will actually be 782.
_____
Computing this by hand doing the initial balance separately from the weekly deposits, I get a total of $46,252.10 using 782 weekly deposits. For that purpose, I tried to figure an equivalent weekly interest rate given monthly compounding and the fact there are 52 5/28 weeks in a year on average.
I suspect the only way to get this to the cent would be to build a spreadsheet with payment dates and interest computation/payment dates. Some months, there would be 5 deposits between interest computations; some years there would be 53 deposits.
