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Insertion of AM's Between 2 Numbers

Question 3For...

Question

Question 3
For the AP –3, –7, –11,… can we find directly $a_{30} - a_{20}$ without actually finding $a_{30} a n d a_{20}$ ? Give the reason for your answer.

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Solution

True.
nth term of an AP, $a_{n} = a + (n - 1) d$
$∴ a_{30} = a + (30 - 1) d = a + 29 d$
$a n d a_{20} = a + (20 - 1) d = a + 19 d$
$N o w, a_{30} - a_{20} = (a + 29 d) - (a + 19 d) = 10 d$
Common difference, d = -7 - (-3) = -7 + 3
= - 4
$∴ a_{30} - a_{20} = 10 (- 4) = - 40$

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