Question

(a) The fifth term of an arithmetic sequence is $40$ and tenth term is $20$. What is the fifteenth term?
(b) How many terms of this sequence make the sum zero?

Answer 1

(a) $x_5=40,x_{10}=20$
$x_{10}-x_5=5d$
$5d=20-40=-20$
$\Rightarrow d=-4$
Now, $x_{15}=x_{10}+5d=20-20=0$
(b) First term, $f=x_5-4d=40-4(-4)=56$
$S_n=\frac{n[2f+(n-1\left)d\right]}{2}$
$\Rightarrow 0=\frac{n[2\times 56+(n-1\left)\right(-4\left)\right]}{2}$
$\Rightarrow n(112-4n+4)=0$
$\Rightarrow n(116-4n)=0$
$\Rightarrow =0,n=29$
Thus, $29$ terms of this sequence make the sum zero.