Question

how many terms of the arithmetic series 10 + 8 + 6 +... will make the sum 24?

Answer 1

$\text{The formula for the sum of a series is given by}\\s_n= \frac{n}{2}(2a+(n-1)d)-(1)\\\text{where a = 10, d = 8 - 10 = -2 and n = 24, therefore }\\24 = \frac{n}{2}(2(10)+(n-1)-2)-(2)\\=48 =n(20-2n+2)\\=48 =-2n^2+22n\\=-2n^2+22n-48\\\text{Dividing through by -2 and factorising we have}\\(n-3)(n-8)=0,\text{therefore n=3 and n=8}$