The 10th term of an arithmetic progression is _27 and 5th term is _12 ,what is the 18th term ?find also the sum of its 25 term
a + 9d = 27
a + 4d = 12
subtracting equations ... 5d = 15
solve for d , then substitute back to find a
Adjust as necessary if you really meant -27 and -12
Art
To find the next term in an arithmetic progression, you need to know the common difference between each term. With that information, we can use the formula:
nth term = a + (n - 1)d
where the nth term is the term you want to find, a is the first term, n is the position of the term, and d is the common difference.
In this case, let's denote the 10th term as a10 and the 5th term as a5. We are given that a10 = -27 and a5 = -12. We need to determine the common difference (d) first.
To find the common difference (d), we can subtract the 5th term from the 10th term:
d = a10 - a5
d = (-27) - (-12)
d = -15
Now that we have the common difference, we can find the 18th term (a18). Plugging the values into the formula:
a18 = a + (n - 1)d
a18 = (-27) + (18 - 1)(-15)
a18 = -27 + 17(-15)
a18 = -27 - 255
a18 = -282
Therefore, the 18th term is -282.
To find the sum of an arithmetic progression, we need to use the formula:
Sum of n terms = (n/2)(2a + (n - 1)d)
In this case, we want to find the sum of 25 terms (Sn). Plugging the values into the formula:
Sn = (25/2)(2a + (25 - 1)d)
Sn = (25/2)(2(-27) + (25 - 1)(-15))
Sn = (25/2)(-54 + (24)(-15))
Sn = (25/2)(-54 - 360)
Sn = (25/2)(-414)
Sn = -5175
Therefore, the sum of the 25 terms is -5175.