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प्रश्न
Find the middle term of the AP 6, 13, 20, …., 216.
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उत्तर
The given AP is 6,13,20,........,216.
First term, a = 6
Common difference, d =13- 6 = 7
Suppose these are n terms in the given AP. Then,
an = 216
⇒ 6+(n-1) × 7 = 216 [ an = a + (n-1) d]
⇒ 7 (n-1) = 216 -6 =210
⇒ n-1`=210/7 =30`
⇒ n= 30+1 =31
Thus, the given AP contains 31 terms,
∴ Middle term of the given AP
`=((31+1)/2)`th term
= 16th term
= 6+ (16-1) × 7
= 6+105
=111
Hence, the middle term of the given AP is 111.
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