Q) Find the middle term of A.P 6,13, 20, ……., 230.

[Q 21B – Sample Question Paper – CBSE Board 2026]

Ans:

Step 1: given progression is: 6,13, 20, ……., 230

Here, we can see that first term, a = 6

and the common difference, d = 13 – 6 = 7

Step 2: Let’s consider there are n terms in all

hence, the value of n^th term is the last term of AP i.e. 230 (given)

Since, we know that n^th term of an AP, T_n  =  a + (n – 1) d

Therefore, 230 = (6)  + (n – 1) (7)

∴ 7 (n -1) = 230 – 6 = 224

∴ (n – 1) = = 32

∴ n = 32 + 1 = 33

Step 3: Since, there are 33 terms in the given AP, its middle most term will be 17th term, where 16 terms will be on its left hand side and 16 terms will be on the right hand side.

Let’s find the value of this 17th term of the AP, whose first term, a is 6 and common difference, d is 7

Since n^th term of an AP, T_n  =  a + (n – 1) d

∴ T₁₇  =  (6) + (17 – 1) (7) = 6 + 16 x 7

∴ T₁₇ =  = 6 + 112 = 118

Therefore, the 17th term is middle most term of the AP and its value is 118.

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