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.
Answer:
7.814 * 10^6
Step-by-step explanation:
Move the decimal point (which is at the end of the number) six places to the left so that you have one non-zero digit to the left of the decimal point. The number of places it is moved to the left is the exponent. Since it is moved to the left it is a positive exponent.
Answer:
200
Step-by-step explanation:
3/16= .1875
Take the amount of paint you have, 37.5, and divide it by the amount of space, .1875
37.5/.1875= 200
Answer:24 or 4
Step-by-step explanation:
2x2=4 4x6=24 24 or 4
Answer:
60
Step-by-step explanation:
6600 x 10% = 60&$;#;,$:#&#>$
