Find the sum of the 25th term to 50th term of the arithmetic progression 28,23,18, ...
You have an AS where a=28 and d= -5
Find the sum of the first 50 terms using your formula, and then the sum of the first 24 terms.
Subtract the two.
(you should get 7525 - 2052 = 5473 )
The progression lists stops on the downtown 1 train in New York. The next number in the sequence is 14, but that's the last numeric stop.
Try a real New York high school exam question: Complete the progression:
4,14,34,42,blank, blank.
To find the sum of an arithmetic progression, we can use the formula:
S = (n/2)(a + l),
where S is the sum of the terms, n is the number of terms, a is the first term, and l is the last term.
Given that the arithmetic progression has a first term of 28 and a common difference of d = (23 - 28) = -5 (since each term decreases by 5), we need to find the 25th term and the 50th term.
The nth term (Tn) of an arithmetic progression is given by the formula:
Tn = a + (n - 1)d,
where Tn is the nth term, a is the first term, n is the position of the term in the arithmetic sequence, and d is the common difference.
So, to find the 25th term:
T25 = 28 + (25 - 1)(-5)
= 28 + 24(-5)
= 28 - 120
= -92.
Similarly, to find the 50th term:
T50 = 28 + (50 - 1)(-5)
= 28 + 49(-5)
= 28 - 245
= -217.
Now that we know the first term (28), the last term (-217), and the number of terms (50 - 25 + 1 = 26), we can find the sum of the 25th term to the 50th term:
S = (n/2)(a + l)
= (26/2)(28 - 217)
= (13)(-189)
= -2,457.
Therefore, the sum of the 25th term to the 50th term of the arithmetic progression 28, 23, 18, ... is -2,457.