The 4th term of an ap is 15 while the 7th term is 27, find the sum of the 9th and 10th term.
so 4n-1
9th term would be 35 and 10th term would be 39. The sum is 74. I'm in grade four. I just figured it out.
To find the sum of the 9th and 10th terms of an arithmetic progression (AP), we need to determine the common difference (d) and then find the values of the terms.
Given that the 4th term is 15 and the 7th term is 27, we can use these terms to find the common difference.
Step 1: Finding the common difference (d)
The formula to find the nth term (Tn) of an AP is:
Tn = a + (n-1)d
Using the 4th term:
T4 = a + 3d = 15
Using the 7th term:
T7 = a + 6d = 27
We can solve these equations simultaneously to find the values of 'a' and 'd'.
Subtracting the first equation from the second equation, we get:
(a + 6d) - (a + 3d) = 27 - 15
3d = 12
d = 12/3
d = 4
Step 2: Finding the 9th and 10th terms
Now that we have the common difference (d = 4), we can calculate the value of the 9th term (T9) and the 10th term (T10).
Using the formula: Tn = a + (n-1)d
For the 9th term (n = 9):
T9 = a + (9-1) * 4
T9 = a + 32
For the 10th term (n = 10):
T10 = a + (10-1) * 4
T10 = a + 36
Step 3: Finding the sum of the 9th and 10th terms
The sum of the 9th and 10th terms can be calculated by adding T9 and T10.
(T9 + T10) = (a + 32) + (a + 36)
(T9 + T10) = 2a + 68
Therefore, the sum of the 9th and 10th terms is 2a + 68.