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Question
In an A.P., the first term is 12 and the common difference is 6. If the last term of the A.P. is 252, then find its middle term.
Solution
Given, First term, a = 12
Common difference, d = 6
Last term, an = 252
Since, an = a + (n – 1)d
⇒ 252 = 12 + (n – 1) 6
⇒ `240/6` = n – 1
⇒ n = 41
Middle term = `(n + 1)/2`
= `(41 + 1)/2`
= 21st term
Now, a21 = a + (21 – 1)d
= 12 + 20 × 6
= 12 + 120
= 132
Hence, middle term is 132.
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