The fourth term of an AP is 37 and the 6th term is 12 more than the fourth term. Find the first and seventh term
To find the first and the seventh term of an Arithmetic Progression (AP), we need to find the common difference (d) first.
Given that the fourth term (a₄) is 37, we know that:
a₄ = a + 3d (where a is the first term and d is the common difference)
Similarly, the sixth term (a₆) is 12 more than the fourth term (a₄ + 12):
a₆ = a₄ + 12
= a + 3d + 12
Now, we can set up two equations using the given information:
a₄ = 37 --> Equation 1
a₆ = a + 3d + 12 --> Equation 2
Since we have two equations with two unknowns (a and d), we can solve for a and d.
Subtracting equation 1 from equation 2, we get:
(a + 3d + 12) - (a + 3d) = 37 - 0
Simplifying the equation:
12 = 37
This is not possible. Hence, the given information is not consistent.
Please double-check the values provided for the fourth term and the sixth term to ensure there are no typographical errors or any missing information.