In an AP T7:T3=13:5 find APeace
To find the missing term in an arithmetic progression (AP), we can use the concept of ratios. In an AP, the common difference (d) between consecutive terms remains constant.
In the given AP T7:T3 = 13:5, we need to find the 6th term (T6). To do this, we need to determine the common difference.
To find the common difference, we can use the formula:
Common Difference (d) = (T7 - T3) / (7 - 3)
Substituting the given values, we get:
d = (13 - 5) / (7 - 3)
d = 8 / 4
d = 2
So, the common difference (d) is 2.
To find the 6th term (T6) in the AP, we use the formula:
Tn = a + (n - 1) * d
Where:
Tn = the nth term
a = the first term
n = the position of the term in the AP
d = the common difference
We are given T3 = 5, so substituting these values, we get:
T6 = 5 + (6 - 1) * 2
T6 = 5 + 5 * 2
T6 = 5 + 10
T6 = 15
Therefore, the 6th term (APeace) in the arithmetic progression is 15.