Answer:
492,800
Step-by-step explanation:
Given ith term of an arithmetic sequence as shown:
ai = a(i-1)+2
and a1 = 5
When i = 2
a2 = a(2-1)+2
a2 = a1+2
a2 = 5+2
a2 = 7
When i = 3
a3 = a(3-1)+2
a3 = a2+2
a3 = 7+2
a3 = 9
It can be seen that a1, a2 and a3 forms an arithmetic progression
5,7,9...
Given first term a1 = 5
Common difference d = 7-5= 9-7 = 2
To calculate the sum of the first 700 of the sequence, we will use the formula for finding the sum of an arithmetic sequence.
Sn = n/2{2a1+(n-1)d}
Given n = 700
S700 = 700/2{2(5)+(700-1)2}
S700 = 350{10+699(2)}
S700 = 350{10+1398}
S700 = 350×1408
S700 = 492,800
Therefore, the sum of the first 700 terms in the sequence is 492,800
Answer:
Step-by-step explanation: You just have to isolate x on one side of the equation
4x - 12 = -5x + 51 Add 12 to both sides to isolate 4x on the left
4x = -5x + 63 Add -5x to both sides to isolate both the variable and numbers on their respective sides
9x = 63 Now divide each side by 9 to isolate x and find the answer
x = 7
Based on what John likes I would suggest he move to areas up north. Like for example Canada, Alaska, Iceland, etc.
Answer:
Choice B. log 4^x = log 17
Step-by-step explanation:
Solve 4^x=17
x is in the exponent... so the only operation to bring the x down is the Logarithm
log 4^x = log 17 take log of both sides
then x* log 4 = log 17
and then x = (log 17)/(log 4)
Answer:
aₙ = 4(-1)ⁿ⁻¹(3)ⁿ⁻¹
Step-by-step explanation:
The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
We can get the value for r by dividing aₙ by aₙ₋₁.
a₄/a₃ = -108/36
a₄/a₃ = -3
r = -3
aₙ = 4(-3)ⁿ⁻¹
aₙ = 4(-1)ⁿ⁻¹(3)ⁿ⁻¹
The (-1)ⁿ⁻¹ term makes even-numbered terms negative.
