# Find the sum of all the 11 terms of an AP whose middle most term is 30. - Mathematics

Sum

Find the sum of all the 11 terms of an AP whose middle most term is 30.

#### Solution

Since the total number of terms (n) = 11 ......[odd]

Middle most term = (n + 1)^("th")/2 term

= ((11 + 1)/2)^("th") term

= 6th term

Given that a6 = 30  .......[∵ an = a + (n − 1)d]

⇒ a + (6 - 1)d = 30

⇒ a + 5d = 30

∵ Sum of n terms of an AP

S_n = n/2[2a + (n - 1)d]

∴ S_11 = 11/2[2a + (11 - 1)d]

= 11/2(2a + 10d)

= 11(a + 5d)

= 11 xx 30

= 330  .....[From equation (i)]

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 29 | Page 54
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