The common difference is d = 4 because we add 4 to each term to get the next one.
The starting term is a1 = 3
The nth term of this arithmetic sequence is
an = a1 + d(n-1)
an = 3 + 4(n-1)
an = 3 + 4n-4
an = 4n - 1
Plug in n = 25 to find the 25th term
an = 4n - 1
a25 = 4*25 - 1
a25 = 100 - 1
a25 = 99
So we're summing the series : 3+7+11+15+...+99
We could write out all the terms and add them all up. That's a lot more work than needed though. Luckily we have a handy formula to make things a lot better
The sum of the first n terms is Sn. The formula for Sn is
Sn = n*(a1+an)/2
Plug in n = 25 to get
Sn = n*(a1+an)/2
S25 = 25*(a1+a25)/2
Then plug in a1 = 3 and a25 = 99. Then compute to simplify
S25 = 25*(a1+a25)/2
S25 = 25*(3+99)/2
S25 = 25*(102)/2
S25 = 2550/2
S25 = 1275
The final answer is 1275
Answer is A. To simplify you multiply numerator and denominator by the conjugate of the denominator.
I am 99% sure. Good luck.
The number is 5. 27-12=15/3=5 is how you get the answer.
Answer:
21 x 21 = 441
Step-by-step explanation:
Whenever there is an exponent that is the many times you multiply the base by itself to.
18) Let x be the number of coins in the pouch:
3x + 3 = 9; subtract 3 from each side:
3x + - 3 = 9 -3
3x = 6 . Now divide both side by 3:
x = 2 (in each pouch we have 2 coins)
19) SAME logic:
4x + 1 = 2x + 7; subtract 1 from each side:
4x + 1 - 1 = 2x + 7 - 1
4x = 2x + 6; now subtract 2x from each side:
4x - 2x = 2x + 6 - 2x
2x = 6 and x = 3 (each pouch contains 3 coins)
