Two ap has the same common difference if the first term of the first progression is 3 and that of the other is 8 then the difference between their 3rd term is
Option
A)2
B)3
C)4
D)5
The difference between the corresponding first terms = 8-3 = 5
The difference between the corresponding 2nd terms = 8+d-(3+d) = 5
ummh, can you see what his happening here?
To find the difference between the third terms of two arithmetic progressions (APs) with the same common difference but different first terms, we need to calculate the third term of each AP and then find the difference between them.
Let's start with the first arithmetic progression (AP) where the first term is 3. We know that the common difference between terms is the same as the other AP. Let's denote the common difference as 'd'.
The first term (a1) of the first AP is 3.
The second term (a2) can be found using the formula: a2 = a1 + d.
Since a1 = 3, we have a2 = 3 + d.
Similarly, the third term (a3) can be found using the same formula: a3 = a2 + d.
Substituting the value of a2, we get a3 = (3 + d) + d = 3 + 2d.
Now let's look at the second arithmetic progression (AP) with the first term of 8. We already know the common difference (d) from the first AP.
The first term (b1) of the second AP is 8.
The second term (b2) can be found using the formula: b2 = b1 + d.
Since b1 = 8, we have b2 = 8 + d.
Similarly, the third term (b3) can be found using the same formula: b3 = b2 + d.
Substituting the value of b2, we get b3 = (8 + d) + d = 8 + 2d.
Finally, to find the difference between the third terms (a3 and b3) of these two APs, we subtract the value of a3 from b3: b3 - a3.
(b3 - a3) = (8 + 2d) - ( 3 + 2d)
= 8 + 2d - 3 - 2d
= 5
So, the difference between the third term of the two arithmetic progressions is 5.