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

Solution:

Given, the middle term of an AP is 30.

We have to find the sum of all the 11 terms of an AP.

There are 11 terms in total. So, the middle term will be the 6th term.

The nth term of the series in AP is given by

aₙ = a + (n - 1)d

a + (6 - 1)d = 30

a + 5d = 30 ---------- (1)

The sum of the first n terms of an AP is given by

Sₙ = n/2[2a + (n-1)d]

The sum of the first 11 terms of the series is

S₁₁ = 11/2[2a + (11 - 1)d]

= 11/2[2a + 10d]

Taking out common term,

= (11/2)2[a + 5d]

Cancelling out common term,

S₁₁ = 11[a + 5d]--------- (2)

Substituting (1) in (2)

= 11(30)

= 330

Therefore, the sum of the first 11 terms of an AP is 330.

✦ Try This: Find the sum of all the 13 terms of an AP whose middle most term is 47

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 29

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

Summary:

An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. The sum of all the 11 terms of an AP whose middle most term is 30 is 330

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