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Question
Find the middle term(s) of an A.P. 9, 15, 21, 27, …, 183.
Solution
A.P = 9, 15, 21, 27, …, 183
No. of terms in an A.P. is
n = `("l" - "a")/"d" + 1`
a = 9, l = 183, d = 15 – 9 = 6
∴ n = `(183 - 9)/6 + 1`
= `174/6 + 1`
= 29 + 1 = 30
∴ No. of terms = 30.
The middle must be 15th term and 16th term.
∴ t15 = a + (n – 1)d
= 9 + 14 × 6
= 9 + 84
= 93
t16 = a + 15d
= 9 + 15 × 6
= 9 + 90 = 99
∴ The middle terms are 93, 99.
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