pls help me out in dis ? dat says The 9th term of an Ap is 52 while d 12th term is 70 find d sum of it's 20th term?
1220
1220
Why did the math book feel sad? Because it had too many problems! But don't worry, I'm here to help. Let's tackle this arithmetic progression (AP) conundrum together.
To find the sum of the 20th term of an AP, we first need to find the common difference (d). We can do this by subtracting the 9th term from the 12th term:
70 - 52 = 18
Now that we know the common difference, we can find the 20th term. We'll use the formula for the nth term of an AP:
an = a1 + (n - 1) * d
Here, an represents the term we want to find (the 20th term), a1 represents the first term, which is unknown, n represents the position of the term (20 in this case), and d represents the common difference (18).
Now, let's plug in the values and solve for a1:
a20 = a1 + (20 - 1) * 18
a20 = a1 + 19 * 18
Since the first term (a1) is unknown, we'll have to solve for it using the information given.
We know that the 9th term is 52. We can use this information to determine a1:
a9 = a1 + (9 - 1) * 18
52 = a1 + 8 * 18
52 = a1 + 144
Let me grab my handy calculator...
a1 = -92
Now that we know a1, we can substitute it back into the formula for the 20th term:
a20 = -92 + 19 * 18
a20 = -92 + 342
a20 = 250
Voila! The 20th term is 250. Now, to find the sum of the first 20 terms of the AP, we can use the formula:
Sn = (n/2)(a1 + an)
Just plug in the numbers:
S20 = (20/2)(-92 + 250)
S20 = 10 * 158
S20 = 1580
The sum of the 20th term of the AP is 1580. Ta-da!
To find the sum of the 20th term of the arithmetic progression (AP), we need to first determine the common difference (d).
Given that the 9th term (a9) of the AP is 52 and the 12th term (a12) is 70, we can use these values to find the common difference.
We know that the general formula for an AP is: an = a1 + (n - 1) * d, where an represents the nth term, a1 is the first term, n is the term number, and d is the common difference.
Using this formula, we can set up two equations based on the given information:
a9 = a1 + (9 - 1) * d ...(equation 1)
a12 = a1 + (12 - 1) * d ...(equation 2)
Substituting the given values into the equations, we have:
52 = a1 + 8d ...(equation 1)
70 = a1 + 11d ...(equation 2)
Now, we can solve these two equations simultaneously to find the values of a1 and d. Subtracting equation 1 from equation 2 eliminates a1 and gives:
70 - 52 = a1 + 11d - a1 - 8d
18 = 3d
d = 6
Having found the common difference (d = 6), we can now find the first term (a1) using equation 1:
52 = a1 + 8 * 6
52 = a1 + 48
a1 = 52 - 48
a1 = 4
Now that we know the first term (a1 = 4) and the common difference (d = 6), we can use the formula to find the 20th term (a20) of the AP:
a20 = a1 + (20 - 1) * d
a20 = 4 + 19 * 6
a20 = 4 + 114
a20 = 118
Therefore, the 20th term of the AP is 118.
To find the sum of the first 20 terms of an AP, we use the formula:
Sn = (n/2) * (2a1 + (n - 1) * d)
Substituting the known values, we get:
S20 = (20/2) * (2*4 + (20 - 1) * 6)
S20 = 10 * (8 + 19 * 6)
S20 = 10 * (8 + 114)
S20 = 1220
Hence, the sum of the 20th term of the arithmetic progression is 1220.
S20 = 20/2 (T1+T20)
d = (T12-T9)/3
T1 = T9-8d
Now just plug and chug.