Three terms of geometric sequence: T1,T2 and T3.
If T2=T1+4 and T3=T2+9 determine the values of T1,T2 and T3.
ar = a+4
ar^2 = ar+9
Now just solve for a and r
How do i solve for a and r ?
To determine the values of T1, T2, and T3 in a geometric sequence, we can use the given information:
1. Start with the given equation T2 = T1 + 4. This means that the second term of the sequence is equal to the first term plus 4.
2. Use this equation to substitute the value of T2 in the equation T3 = T2 + 9. We now have T3 = (T1 + 4) + 9.
3. Simplify the equation: T3 = T1 + 13.
4. Since this equation is still in terms of T1 and T3, we need one more equation to solve for both T1 and T3. Let's look at the relationship between T2 and T3.
5. We can see that T3 = T2 + 9. Plugging in T2 = T1 + 4, we get T3 = (T1 + 4) + 9.
6. Simplifying this equation, we get T3 = T1 + 13.
7. We now have two equations with the same form: T3 = T1 + 13. Since both equations are equal to T3, they are equal to each other:
T1 + 13 = T1 + 13.
8. Subtracting T1 from both sides, we get 13 = 13. This equation is always true, which means that T1 can take any value.
9. Since T1 can be any value, there is no unique solution for T1, T2, and T3. However, we can write the equations for T2 and T3 in terms of T1:
T2 = T1 + 4,
T3 = T1 + 13.
So, for any given value of T1, T2 will be T1 + 4, and T3 will be T1 + 13.