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.
Mathematics
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3 stepsLet's find the number of terms in the series.
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.Substitute the given values into the formula.
Sₙ = 252
a = -16
l = 72252 = (n/2)(-16 + 72)
Simplify the expression and solve for n.
252 = (n/2)(56)
252 = 28nTo find n, divide both sides by 28.
n = 252 / 28
n = 9The number of terms in the series is 9.
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