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Find the middle term of the AP 213, 205,...

Find the middle term of the AP `213, 205, 197, …, 37.`

A

`124`

B

`125`

C

`126`

D

`127`

Text Solution

Verified by Experts

The correct Answer is:
B
Here a = 213 and d = (205-213) = -8.
Let the given AP contain n terms. Then,
`T_(n) = 37 rArr a + (n-1)d = 37`
`rArr 213 + (n-1) xx (-8) = 37`
`rArr 221-8n = 37`
`rArr 8n = 221 -37 = 184 rArr n = 23.`
Thus, the given AP contains 23 terms.
`therefore` its middle term ` = (1)/(2) (23+ 1)` th term = 12th term.
So, middle term ` = T_(12) = (a + 11d)`
`= 213 + 11 xx (-8) = 213-88 = 125.`
Hence, the middle term is `125.`
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