find the 7th term of an AP. whose 4th term is 5 and the common difference is -2
A4 = a+3d
A7 = a+6d = A4 + 3d = 5 + 3(-2) = -1
Thanks for helping me.
To find the 7th term of an arithmetic progression (AP), we can use the formula:
tn = a + (n - 1) * d
Where:
tn = the nth term of the AP
a = the first term of the AP
n = the term number
d = the common difference between the terms
Given:
4th term (n = 4) = 5
Common difference (d) = -2
Let's begin:
Using the given information, we can substitute the values into the formula:
5 = a + (4 - 1) * (-2)
Simplify the equation:
5 = a + 3 * (-2)
5 = a - 6
Now, solve for the first term (a):
a = 5 + 6
a = 11
Now that we have the value of the first term (a = 11), we can find the 7th term using the formula:
t7 = a + (7 - 1) * d
Substitute the values into the formula:
t7 = 11 + (7 - 1) * (-2)
Simplify the equation:
t7 = 11 + 6 * (-2)
t7 = 11 + (-12)
t7 = -1
Therefore, the 7th term of the given arithmetic progression (AP) is -1.
To find the 7th term of an arithmetic progression (AP), we can use the formula:
\[ a_n = a_1 + (n-1) \cdot d \]
Where:
- \( a_n \) represents the nth term of the AP
- \( a_1 \) represents the first term of the AP
- \( n \) represents the position of the term in the AP
- \( d \) represents the common difference between the terms of the AP
Given:
- 4th term (\( a_4 \)) = 5
- Common difference (\( d \)) = -2
We need to find the 7th term, which corresponds to \( a_7 \).
We can start by finding \( a_1 \) using the formula:
\[ a_4 = a_1 + (4-1) \cdot d \]
Substituting the given values, we have:
\[ 5 = a_1 + 3 \cdot (-2) \]
\[ 5 = a_1 - 6 \]
\[ a_1 = 11 \]
Now that we have found \( a_1 \), we can calculate the 7th term (\( a_7 \)) using the same formula:
\[ a_7 = a_1 + (7-1) \cdot d \]
Substituting the values we know:
\[ a_7 = 11 + 6 \cdot (-2) \]
\[ a_7 = 11 - 12 \]
\[ a_7 = -1 \]
Therefore, the 7th term of the given arithmetic progression is -1.