First two terms of AP are -5 and -7.find its 11th term
To find the 11th term of an arithmetic progression (AP), we need to know the common difference (d) between consecutive terms. The common difference (d) is the constant value added to each term to get the next term in the sequence.
In this case, we know that the first term (a₁) of the AP is -5, and the second term (a₂) is -7. To find the common difference, we can subtract the first term from the second term:
d = a₂ - a₁
d = -7 - (-5)
d = -7 + 5
d = -2
Now that we know the common difference (d = -2), we can find the 11th term by using the formula:
aₙ = a₁ + (n - 1) * d
The formula gives us the nth term (aₙ) of the AP, where n is the position of the term in the sequence.
To find the 11th term (a₁₁), substitute the values into the formula:
a₁₁ = a₁ + (11 - 1) * d
a₁₁ = -5 + (10) * (-2)
a₁₁ = -5 - 20
a₁₁ = -25
Therefore, the 11th term of the arithmetic progression is -25.