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

Sum

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

#### 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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