Question

1. In an A.P consisting of 27 terms, the sum of the first three terms is 21 and that of the three middle terms is 93. Find the first term and the common
difference
6,23
5,2
7,3
6,3​

Answer 1

Answer:

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Step-by-step explanation:

Given total number of terms in an AP = 21.

Given that the sum of three terms in the middle is 129.

= > T10 + T11 + T12 = 129

= > a + 9d + a + 10d + a + 11d = 129

= > 3a + 30d = 129

= > a + 10d = 43 ----- (1)

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Given that sum of last three terms is 237.

= > T19 + T20 + T21 = 237

= > a + 18d + a + 19d + a + 20d = 237

= > 3a + 57d = 237

= > a + 19d = 79 ----- (2)

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On solving (1) & (2), we get

= > a + 10d = 43

= > a + 19d = 79

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-9d = -36

d = 4.

substitute d = 4 in (1), we get

= > a + 10d = 43

= > a + 10(4) = 43

= > a + 40 = 43

= > a = 43 - 40

= > a = 3.

Therefore, The first term is 3 and Common difference = 4.

The required AP is 3,7,11....

Hope this helps!