If the first and last term of an A.P are -3 and 145 respectively. If the common difference is 4, find the 12th term
-3 + 11*4 = ___
To find the 12th term of the arithmetic progression (A.P.), we need to use the formula for the nth term in an A.P., which is given by:
An = A1 + (n - 1) * d
where:
An = nth term of the A.P.
A1 = first term
n = position of the term
d = common difference
Given that the first term (A1) is -3, the common difference (d) is 4, and we want to find the 12th term (n = 12), we can substitute these values into the formula:
A12 = -3 + (12 - 1) * 4
A12 = -3 + (11) * 4
A12 = -3 + 44
A12 = 41
Therefore, the 12th term of the arithmetic progression is 41.
To find the 12th term of an arithmetic progression (A.P.) given the first and last terms and the common difference, you can use the formula:
tn = a + (n - 1)d
where tn represents the nth term, a is the first term, n is the position of the term, and d is the common difference.
In this case:
a = -3 (first term)
l = 145 (last term)
d = 4 (common difference)
Since the last term is given, we can relate it to the first term and the common difference using the formula for the nth term:
l = a + (n - 1)d
Substituting the known values:
145 = -3 + (n - 1)4
Simplifying:
145 = -3 + 4n - 4
145 + 3 + 4 = 4n
152 = 4n
Dividing both sides by 4:
n = 152/4
n = 38
Now that we know the position of the 12th term is 38, we can find this term using the formula tn = a + (n - 1)d:
t12 = a + (12 - 1)d
t12 = -3 + 11(4)
t12 = -3 + 44
t12 = 41
Therefore, the 12th term of the arithmetic progression is 41.