Question

The 10th term of an arithmetic sequence is 65 and its 15th term is 20. Find 20th term of this arithmetic sequence.

Answer 1

15th term can be obtained by adding 10th term and 5 times the common difference $(\because 15-10=5)$

$\Rightarrow x_{15}=x_{10}+5d$

$\Rightarrow 20=65+5d$

$\Rightarrow -45=5d$

$\Rightarrow d=\frac{-45}{5}=-9$ (1 mark)

$\Rightarrow$ 20th term can be obtained by adding 15th term & 5 times the common difference

$\Rightarrow x_{20}=x_{15}+5d$

=20+5(-9)

=20-45

=-25 ( 1 mark)