The 10th and 15th terms of an AP are -5 and -7 1/2 respectively.What is the sum of the first 20 terms?[WAEC]
once is enough, but what the heck?
the common difference is d = (7 1/2 + 5)/5 = ____
a = -5 - 9d = ___
S20 = 20/2 (2a+19d) = ___
The first term of an AP is 6 and the fifth term is 18. Find the number of terms in the series having a sum of 162 solve it
Solve this:The first term of an AP is 6 and the fifth term is 18. Find the number of terms in the series having a sum of 162
To find the sum of the first 20 terms of an arithmetic progression (AP), we can make use of the formula:
Sum of AP = (n/2) * (first term + last term),
where n is the number of terms in the AP.
First, let's find the common difference (d) between the terms of the AP.
The 10th term is given as -5, and the 15th term is given as -7 1/2.
To find the common difference, we subtract the 10th term from the 15th term:
-7 1/2 - (-5) = -7 1/2 + 5 = -2 1/2.
Therefore, the common difference (d) between the terms is -2 1/2.
Now, let's find the first term (a) of the AP.
The 10th term is given as -5, and the common difference is -2 1/2.
To find the first term, we can use the formula:
a = nth term - (n-1) * common difference.
Plugging in the values:
a = -5 - (10-1) * (-2 1/2)
= -5 - 9 * (-2 1/2)
= -5 - 9 * (-5/2)
= -5 + 45/2
= -5 + 22 1/2
= 17 1/2.
Therefore, the first term of the AP is 17 1/2.
Now, we can find the sum of the first 20 terms using the formula mentioned earlier:
Sum of AP = (n/2) * (first term + last term).
Plugging in the values:
Sum of AP = (20/2) * (17 1/2 + last term).
To find the last term, we can use the formula:
last term = first term + (n-1) * common difference.
Plugging in the values:
last term = 17 1/2 + (20-1) * (-2 1/2)
= 17 1/2 + 19 * (-2 1/2)
= 17 1/2 + 19 * (-5/2)
= 17 1/2 + 19 * (-5/2)
= 17 1/2 - 95/2
= 17 1/2 - 47 1/2
= -30.
Now, we can substitute the values into the sum formula:
Sum of AP = (20/2) * (17 1/2 + (-30))
= 10 * (-12 1/2)
= 10 * (-12 - 1/2)
= 10 * (-24/2 - 1/2)
= 10 * (-25/2)
= -250/2
= -125.
Therefore, the sum of the first 20 terms of the given arithmetic progression is -125.