Answer: 257
Step-by-step explanation:
Given that:
a3 = 59
a7 = 103
The nth term of an Arithmetic Progression (A. P) is given by:
an = a1 + (n-1)d
Where a1 = first term of the sequence ;
d = common difference
Therefore a3 = 59 can be represented thus:
a3 = a1 + (3-1)d = 59
a3 = a1 + 2d = 59 - - - - (1)
a7 = 103
a7 = a1 + (7-1)d = 103
a7 = a1 + 6d = 103 - - - - - (2)
Subtracting (2) from (1)
(2d - 6d) = (59 - 103)
-4d = - 44
d = 11
Substitute d= 11 into (1)
a1 + 2d =59
a1 + 2(11) = 59
a1 + 22 = 59
a1 = 59 - 22
a1 = 37
The 21st term:
a21 = a1 + (21 - 1)d
a21 = 37 + 20(11)
37 + 220 = 257
After combining like terms:
-0.7k + 1 = 7.8
Subtract the 1 from both sides:
-0.7k = 6.8
Divide by -0.7 from both sides:
k = -9.7142, simplified is -9.7
Checked Answer:
-0.7(-9.7) = 6.79, simplified is 6.8
Hello from MrBillDoesMath!
Answer:
x = 50
Discussion:
(4x +5) ( 2x - 2) = 8x^2 - 8x + 10x - 10
= 8x^2 + 2x - 10 (A)
(16x^8)/(2x^6) + 90 = 8x^2 + 90 (B)
Setting (A) = (B) gives
8x^2 + 2x - 10 = 8x^2 + 90
Subtract 8x^2 from both sides:
2x - 10 = 90
Add 10 to both sides:
2x = 90 + 10 = 100
Divide both sides by 2:
x = 100/2 = 50
Thank you,
MrB
One fact family is 9 times 9 = 81
