The 5th term of an Arithmetic Progression is 8 and the 12th term is 50. Determine the sequence
d = (T12-T5)/(12-5) = (50-8)/7 = 6
T5 = a+4*6=8, so a = -16
Thus, the sequence is
-16 -10 -4 2 8 ...
In the Arithmetic progression the 5th term is 21 and 12 term is 49
Determine
A)Common difference "d" and the first term
B) fifteen term (15th) term T15 and U 15
C) sum of first s15
Find the fifth term of the sequence -3,6-12....
In an arithmetic sequence, if the 5th term is 7 and the 9th term is -9, find the 12th term.
To determine the sequence of an arithmetic progression given the 5th and 12th terms, we can use the formulas for the nth term and the common difference.
The nth term of an arithmetic progression (AP) is given by:
tn = a + (n - 1)d
Where tn is the nth term, a is the first term, n is the term number, and d is the common difference.
From the given information:
t5 = 8
t12 = 50
Using the formula for the 5th term:
t5 = a + (5 - 1)d
We can substitute the value of t5 into the equation:
8 = a + 4d
Similarly, using the formula for the 12th term:
t12 = a + (12 - 1)d
t12 = a + 11d
Substituting the value of t12:
50 = a + 11d
Now we have a system of two equations with two variables (a and d). Solving these equations will give us the values of a and d, from which we can determine the sequence.
Let's solve the system of equations:
Equation 1: 8 = a + 4d
Equation 2: 50 = a + 11d
We can subtract equation 1 from equation 2 to eliminate a:
50 - 8 = (a + 11d) - (a + 4d)
42 = 7d
Dividing both sides by 7:
42/7 = d
6 = d
Now we can substitute the value of d back into equation 1 to solve for a:
8 = a + 4(6)
8 = a + 24
a = 8 - 24
a = -16
So, the first term (a) is -16 and the common difference (d) is 6.
The sequence can be written as:
-16, -10, -4, 2, 8, 14, 20, 26, 32, 38, 44, 50