The sum of the first n terms of an arithmetic progression is 252. If the first term is –16 and the last term is 72, find the number of terms in the series.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Let's find the number of terms in the series.
Step 1: Write the formula for the sum of an arithmetic progression when the first and last terms are known.
Sₙ = (n/2)(a + l)
where Sₙ is the sum of n terms, a is the first term, l is the last term, and n is the number of terms.
Step 2: Substitute the given values into the formula.
Sₙ = 252
a = -16
l = 72
252 = (n/2)(-16 + 72)
Step 3: Simplify the expression and solve for n.
252 = (n/2)(56)
252 = 28n
To find n, divide both sides by 28.
n = 252 / 28
n = 9
The number of terms in the series is 9.