To find the sum of the first 20 terms of an arithmetic progression, we need to know the first term and the common difference.
Let's say the first term is a and the common difference is d.
We are given that the 10th term is -5 and the 15th term is -7 1/2.
Using the formula for the nth term of an arithmetic progression:
nth term = a + (n-1)d
We can set up two equations using the given information:
-5 = a + (10-1)d
-7 1/2 = a + (15-1)d
Simplifying the equations:
-5 = a + 9d
-7 1/2 = a + 14d
We can multiply the second equation by 2 to get rid of the fraction:
-15 = 2a + 28d
Now we have a system of three equations:
-5 = a + 9d
-7 1/2 = a + 14d
-15 = 2a + 28d
Solving this system of equations, we find that a = -57/2 and d = 5/2.
Now we have the first term a = -57/2 and the common difference d = 5/2.
The sum of the first 20 terms can be calculated using the formula for the sum of an arithmetic progression:
Sum = (n/2)(2a + (n-1)d)
Substituting n = 20, a = -57/2, and d = 5/2:
Sum = (20/2)(2(-57/2) + (20-1)(5/2))
= 10(-57 + 19(5/2))
= 10(-57 + 95/2)
= 10(-57 + 47.5)
= 10(-9.5)
= -95
Therefore, the sum of the first 20 terms of the arithmetic progression is -95.
The 10th and 15th term of an arithmetic progression are -5 and minus 7 whole number 1 over 2 what is the sum of the 1st 20 term
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