The 3rd term and the 13th term of an arithmetic sequence are -40 and 0 respectively. What is the 28th term of the sequence?
the 8th h term of a geometric sequence are -21 and -189 respectively.what is the 3rd term of the sequence ?
To find the 28th term of the arithmetic sequence, we first need to determine the common difference (d) of the sequence.
The formula for calculating the nth term of an arithmetic sequence is:
An = A1 + (n-1)d
Given that the 3rd term (A3) is -40 and the 13th term (A13) is 0, we can substitute these values into the formula:
A3 = A1 + (3-1)d
-40 = A1 + 2d ...........(equation 1)
Similarly, substituting the values of the 13th term:
A13 = A1 + (13-1)d
0 = A1 + 12d ...........(equation 2)
Now, we have a system of two equations with two unknowns (A1 and d). We can solve these equations simultaneously to determine the values of A1 and d.
From equation 1, we can isolate A1:
A1 = -40 - 2d
Substituting this value of A1 into equation 2:
0 = -40 - 2d + 12d
0 = -40 + 10d
Rearranging the equation:
10d = 40
d = 4
Now that we know the value of the common difference (d = 4), we can substitute it back into either equation 1 or equation 2 to find the value of A1.
Using equation 1:
-40 = A1 + 2(4)
-40 = A1 + 8
A1 = -48
Now that we have the values of A1 and d, we can find the 28th term (A28) using the formula:
A28 = A1 + (28-1)d
A28 = -48 + 27(4)
A28 = -48 + 108
A28 = 60
Therefore, the 28th term of the sequence is 60.
To find the 28th term of the arithmetic sequence, we first need to determine the common difference (d) of the sequence.
We are given the third term (a3) as -40 and the 13th term (a13) as 0.
We can use the formula for the general term of an arithmetic sequence:
an = a1 + (n - 1)d
where:
an is the nth term
a1 is the first term
d is the common difference
n is the position of the term in the sequence
Substituting the given values for the third term and the 13th term, we can create two equations:
-40 = a1 + 2d (1) [Since the third term corresponds to n = 3]
0 = a1 + 12d (2) [Since the 13th term corresponds to n = 13]
Now, we can solve these equations simultaneously to find the values of a1 and d.
From equation (1), we can express a1 in terms of d:
a1 = -40 - 2d
Substituting this value of a1 into equation (2), we get:
0 = (-40 - 2d) + 12d
0 = -40 + 10d
10d = 40
d = 4
Now that we know the common difference (d = 4), we can find the first term (a1) by substituting it back into one of the earlier equations.
Using equation (1), we get:
-40 = a1 + 2(4)
-40 = a1 + 8
a1 = -48
Now we can use the general term formula to find the 28th term (a28) of the arithmetic sequence:
a28 = a1 + (n - 1)d
a28 = -48 + (28 - 1)4
a28 = -48 + 27*4
a28 = -48 + 108
a28 = 60
Therefore, the 28th term of the arithmetic sequence is 60.
there are ten common differences between the 3rd term and the 13th term
the common difference is ... (0 - -40) / 10 = 4
there are 15 common differences between the 13th term and the 28th term