Giving that the first term of an AP is 7 and the 10th term is twice the 2nd number
Calculate the 9th term
The sum of the 10 term
Different between the 9th and the 10th term in an understanding way
To find the common difference (d) of the arithmetic progression (AP), we can use the formula for the nth term of an AP:
nth term = first term + (n - 1) * common difference.
Given that the first term (a₁) is 7, and the 10th term (a₁₀) is twice the second term (a₂), we can write the following equations:
a₁ = 7
a₁₀ = 2a₂
First, let's find the common difference:
a₂ = a₁ + d
7 + d = a₂
Substituting this into the equation for the 10th term:
a₁₀ = 2(7 + d)
a₁₀ = 14 + 2d
Since a₁₀ = 2a₂, we can set up the following equation:
14 + 2d = 2(7 + d)
14 + 2d = 14 + 2d
This equation does not provide any new information. Therefore, we can conclude that the given information is not consistent. There is no unique solution for the common difference, 9th term, or sum of the 10 terms.