Answer :
Final answer:
The number of terms in the arithmetic progression is 18, based on the given information and by solving the equation derived from the formula for the sum of an arithmetic series.
Explanation:
The question asks to determine the number of terms in an arithmetic progression (AP) where the first term (a) is 21 and the last term (l) is -47, and the sum (S) of the series is -234. The sum of an arithmetic series can be found using the formula:
S = n/2 * (a + l), where n is the number of terms, a is the first term, and l is the last term.
Given that S = -234, a = 21, and l = -47, we can substitute these values into the formula and solve for n:
-234 = n/2 * (21 - 47)
-234 = n/2 * (-26)
-9 = n/2
n = -18
Since the number of terms cannot be negative, we must have made an error in our calculation. The correct steps are:
-234 = n/2 * (-26)
-234 = -13n
n = 18
Therefore, there are 18 terms in the arithmetic progression.
