Answer: Option B
Given: T4:T7::2:3
Let's find the common difference (d) of the given AP using the formula:
d = (T7 - T4) / 3 = (3T4 - 2T4) / 3 = T4 / 3
Now, we can find T4 in terms of the first term (a) using the relation Tn = a + (n-1)d:
T7 = a + 6d => 3T4 = a + 9d
Substituting the value of d, we get:
3T4 = a + 3T4 / 3 => 9T4 = a + T4 => a = 8T4
Thus, we have a = 8T4 and d = T4 / 3
Using the same relation Tn = a + (n-1)d, we can find T3 and T11 in terms of T4:
T3 = a + 2d = 8T4 + 2(T4/3) = (26/3)T4T11 = a + 10d = 8T4 + 10(T4/3) = (38/3)T4
Now, we can find T3:T11 as:
T3:T11 = (26/3)T4 : (38/3)T4 = 26:38 = 13:19
Therefore, the correct answer is option B, i.e., T3:T11 = 5:13.If you think the solution is wrong then please provide your own solution below in the comments section .