Let's call 'it' x. 1/2 is equal to one third of x, so we could say that 1/3x = 1/2
Now we just have a simple equation to solve:
1/3x = 1/2
x = (1/2) / (1/3)
Dividing by a rational number (such as 1/3, which is expressed in fraction form) is the same as multiplying by its reciprocal (the reciprocal of a fraction is itself when the numerator and denominator have been swapped). Therefore
x = (1/2) / (1/3) = (1/2) * 3 = 3/2 = 1.5
To check this answer, test the statement. Half is a third of x, where x=1.5:
1.5 / 3 = 0.5 = 1/2
Answer: The term to term rule is an Arithmetic progression for the two question. B) 1Oth term for the first is 30 and for the second series is 59
Step-by-step explanation:
4.1) 3 6 9 12 15
For the sequence above, we can see that the next term is gotten by addition of 3 with the previous term and so It is an Arithmetic progression.
Having in mind the nth term of an AP as Tn = a + (n - 1)d.
where a is the first term =3
And d common difference =3(6-3,9-6,12-9)
10th term=
T10 = 3+ (10 - 1)3.
T10 = 3+ (9)3.
T10 = 3+ 27.
T10 =30
4.2) 5 11 17 23 29
For the sequence above, we can see that the next term is gotten by addition of 6 with the previous term and so It is an Arithmetic progression.
Having in mind the nth term of an AP as Tn = a + (n - 1)d.
where a is the first term =5
And d common difference =6 (11-5, 17-11,23-17)
10th term=
T10 = 5+ (10 - 1)6.
T10 = 5+ (9)6.
T10 = 5+ 54.
T10 =59