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Question
Find the middle term of the AP 10, 7, 4, ……., (-62).
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Solution
The given AP is 10,7,4,.....,-62.
First term, a = 10
Common difference, d = 7 -10 =-3
Suppose these are n terms in the given AP. Then,
an = -62
⇒10+ (n-1) × (-3) = -62 [ an = a + (n-1) d]
⇒ -3 (n-1) =-62 -10 = -72
⇒`n-1 = 72/3 = 24 `
⇒ n = 24 + 1= 25
Thus, the given AP contains 25 terms.
∴ Middle term of the given AP
=` ((25+1)/2) ` th term
= 13 th term
= 10+ (13-1) × (-3)
= 10-36
=-26
Hence, the middle term of the given AP is - 26.
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