For the AP: –3, –7, –11, …, can we find directly a30 – a20 without actually finding a30 and a20? Give reasons for your answer.

Home » For the AP: –3, –7, –11, …, can we find directly a30 – a20 without actually finding a30 and a20? Give reasons for your answer.

For the AP: –3, –7, –11, …, can we find directly a30 – a20 without actually finding a30 and a20? Give reasons for your answer.

Solution:

True

Provided that

The first term, $a=-3$

The common difference, $d=\text{ }{{a}_{2}}~-{{a}_{1}}~=-7\left( -\text{ }3 \right)=-4$

${{a}_{30}}-{{a}_{20}}~=\text{ }a+29d-\left( a\text{ }+\text{ }19d \right)$

$=\text{ }10d$

$=\text{ }-40$

This is so because the difference between any two terms of an AP is proportional to the AP’s common difference.

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