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Question
If s = `"n"/(2)[2"a" + ("n" - 1)"d"]`, the n express d in terms of s, a and n. find d if n = 3, a = n + 1 and s = 18.
Solution
s = `"n"/(2)[2"a" + ("n" - 1)"d"]`
⇒ s = `"an" + ("n"("n" - 1)"d")/(2)`
⇒ s - `"an" = ("n"("n" - 1)"d")/(2)`
⇒ `((2"s" - 2"an")/("n"("n" - 1)))` = d
⇒ d = `(2)/("n"("n" - 1))("s" - "an")`
Given that n = 3, a = n + 1 and s = 18
Since
a = n + 1
⇒ a = 3 + 1
= 4
Substituting we get
⇒ d = `(2)/(3(3 - 1))(18 - (4)(3))`
⇒ d = `(2)/(3(2))(18 - 12)`
⇒ d = `(1)/(3)(6)`
⇒ d = 2.
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