Question

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

Answer 1

This is an arithmetic sequence with $a_1=10, d=-2.$

$S_n=\frac{(2a_1+(n-1)d)n}{2}=24.$

$n^2-11n+24=0.$

$n_1=\frac{11-\sqrt{121-96}}{2}=3.$

$n_2=\frac{11+\sqrt{121-96}}{2}=8.$

3 or 8 terms of this arithmetic series will make the sum 24.