Find the sum of the two middle most terms of the AP: -43,-1,-23,...,413. - Mathematics

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Sum

Find the sum of the two middle most terms of the AP: `- 4/3, -1, -2/3,..., 4 1/3`.

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Solution

Here, first term (a) = `-4/3`

Common difference (d) = `-1 + 4/3 = 1/3`

And the last term (l) = `4/3 = 13/3`   ....`[because n^"th" "term of an AP", l = a_n = a + (n - 1)d]`

⇒ `13/3 = -4/3 + (n - 1)1/3`

⇒ `13 = -4 + (n - 1)`

⇒ `n - 1 = 17`

⇒ `n = 18`   .....[Even]

So, the two middle most terms are `(n/12)^("th")`

And `(n/2 + 1)^("th")`

i.e., `(18/n)^("th")` and `(18/2 + 1)^("th")` terms

i.e., 9th and 10th terms.

∴ `a_9 = a + 8d`

= `- 4/3 + 8(1/3)`

= `(8 - 4)/3`

= `4/3`

And `a_10 = - 4/3 + 9(1/3)`

= `(9 - 4)/3`

= `5/3`

So, sum of the two middle most terms

`a_9 + a_10`

= `4/3 + 5/3`

= `9/3`

= 3

Concept: Sum of First n Terms of an A.P.
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APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 5 Arithematic Progressions
Exercise 5.3 | Q 19 | Page 53
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