How many terms has the A.P whose first term is 15 and the last term is 57 given that the common difference is 3
Let's denote the first term of the arithmetic progression (AP) as a₁, the last term as aₙ, the common difference as d, and the total number of terms as n.
Given:
a₁ = 15
aₙ = 57
d = 3
We can use the formula for the nth term of an arithmetic progression to find the number of terms:
aₙ = a₁ + (n - 1)d
Substitute the given values into the formula:
57 = 15 + (n - 1)(3)
Simplify the equation:
42 = 3n - 3
45 = 3n
n = 15
Therefore, the arithmetic progression has 15 terms.
To find the number of terms in an arithmetic progression (A.P.), we need to use the formula:
n = (last term - first term) / common difference + 1
Given that the first term is 15, the last term is 57, and the common difference is 3, we can substitute these values into the formula:
n = (57 - 15) / 3 + 1
n = 42 / 3 + 1
n = 14 + 1
n = 15
Therefore, the A.P. has 15 terms.