Final answer:
The 5th term of the arithmetic progression is 21, and the 10th term is -27. By using the formula for the nth term of an AP, the common difference is found to be -9.6, which in turn helps to calculate the first term as 59.4.
Step-by-step explanation:
The question involves finding the values of an arithmetic progression (AP). We are given the 5th term (№5) as 21 and the 10th term (№10) as -27 in an AP. Our goal is to find the first term (№1) of this AP.
Let's denote the first term by №1 and the common difference by d. The nth term of an AP can be represented as:
№n = №1 + (n-1) * d
Let's use the information given about the 5th and 10th terms:
№5 = №1 + 4d = 21
№10 = №1 + 9d = -27
Subtracting the first equation from the second, we get:
9d - 4d = -27 - 21
5d = -48
d = -48 / 5
Now we find the first term №1, using the value of d in the equation for №5:
21 = №1 + 4(-48/5)
21 = №1 - 48 * 4 / 5
21 = №1 - 38.4
№1 = 21 + 38.4
№1 = 59.4
Hence, the first term of the AP is 59.4.