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Question
Make a the subject of the formula S = `"n"/(2){2"a" + ("n" - 1)"d"}`. Find a when S = 50, n = 10 and d = 2.
Solution
S = `"n"/(2){2"a" + ("n" - 1)"d"}`
⇒ 2S = n{2a + (n - 1)d}
⇒ `(2"s")/"n"` = 2a + (n - 1)d
⇒ `(2"s")/"n" - ("n" - 1)"d"` = 2a
⇒ `{"S"/"n" - (("n" - 1)"d")/(2)}` = a
Substituting S = 50, n = 10 and d = 2, we get
a = `{"S"/"n" - (("n" - 1)"d")/(2)}`
= `{50/10 - (9 xx 2)/(2)}`
= 5 - 9
= -4.
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