Question

There are 21 terms in an AP. the sum of last three terms is 123 and the sum of three middle term is 69. find the AP​

Answer 1

Step-by-step explanation:

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Answer 2

The required AP is 7,11, 14

Total number of terms in AP = 21.  (Given)

Sum of three terms in the middle is 69.  (Given)

Sum of last three terms is 123. (Given)

T10 + T11 + T12 = 69

a + 9d + a + 10d + a + 11d = 69

3a + 30d = 69

a + 10d = 23 ----- (1)

T19 + T20 + T21 = 123

a + 18d + a + 19d + a + 20d = 123

3a + 57d = 123

a + 19d = 41 ----- (2)

On solving equation (1) & (2), -

a + 10d = 23

a + 19d = 41

-------------------

-9d = -18

d = 3.

Substituting d = 3 in (1),

a + 10d = 23

a + 10(3) = 23

a + 30 = 23

a = 30 - 23

a = 7.

Therefore, The first term is 7 and Common difference = 3.

The required AP is 7,11, 14 ...