Find the middle terms of the sequence formed by all numbers between 9

1.	Find the middle terms of the sequence formed by all numbers between 9 and 95, which leave a remainder 1 when divided by 3. Also, find the sum of the numbers on both sides of the middle term separately.
Answer» The sequence is 10, 13, ..... 94. 94= 10 + (n – 1) 3 ⇒ n = 29 Therefore (29 + 1)/ 2 = 15th term is the middle term Middle term = 10 + 14 × 3 = 52 Sum of first 14 terms = 14/2 [20 + 13 × 3] = 413 Sum of the last 14 terms = 14/2 [110 + 13 × 13] = 1043

Find the middle terms of the sequence formed by all numbers between 9 and 95, which leave a remainder 1 when divided by 3. Also, find the sum of the numbers on both sides of the middle term separately.

Answer»

The sequence is 10, 13, ..... 94.

94= 10 + (n – 1) 3 ⇒ n = 29

Therefore (29 + 1)/ 2 = 15th term is the middle term

Middle term = 10 + 14 × 3 = 52

Sum of first 14 terms = 14/2 [20 + 13 × 3] = 413

Sum of the last 14 terms = 14/2 [110 + 13 × 13] = 1043

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Find the middle terms of the sequence formed by all numbers between 9 and 95, which leave a remainder 1 when divided by 3. Also, find the sum of the numbers on both sides of the middle term separately.

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