In an arithmetic series, the sum of first 11 terms is 44 and that of the next 11 terms is 55. Find the arithmetic series.

Sum of terms =

⇒ 44 =

⇒ 8 = 2a + 10d

⇒ 2a + 10d = 8 ……………………….(1)

Now sum of next 11 terms is 55

Sum of first 22 terms = Sum of first 11 terms + Sum of next 11 terms

⇒ Sum of first 22 terms = 44 + 55 = 99

Sum of terms =

⇒ 99 =

⇒ 9 = 2a + 21d

⇒ 2a + 21d = 9 ……….(1)

Subtracting (1) from (2), we get

⇒ 11d = 1

⇒ d = 1/11

Putting value of d in (1), we get

⇒ 2a + 10(1/11) = 8

⇒ 2a = 8–(10/11)

⇒ 2a = 78/11

⇒ a = 39/11

Therefore, the series is