In an A.P. the third term is 4 times the 1st term
To find the third term of an arithmetic progression (A.P.) when the first term is given, you need to know the common difference of the A.P.
Let's denote the first term as 'a' and the common difference as 'd'. According to the given information, the third term is 4 times the first term.
So, we can write the equation as:
a + 2d = 4a
Now, let's solve this equation to find the value of 'a' and 'd'. Rearranging the equation, we get:
2d = 3a
Dividing both sides by 2, we have:
d = 3a/2
Now, you need more information to solve for the values of 'a' and 'd'.
No unique answer here
a+2d = 4a
2d = 3a
d = 3a/2
start with any value of a, pick an even to avoid fractions, then form your AP
e.g.
let a = 6, then d = 9
AP is 6, 15, 24, 33, ...
let a = -4, d = -6
AP is -4, -10, -16, -22, ...
In each case the 3rd term is 4 times the first.