Insert five numbers between 11 and 29 such that the resulting sequence is an AP.

To find: Five numbers between 11 and 29, which are in A.P.


Given: (i) The numbers are 11 and 29


Formula used: (i) An = a + (n-1)d


Let the five numbers be A1, A2, A3, A4 and A5


According to question 11, A1, A2, A3, A4, A5 and 29 are in A.P.


We can see that the number of terms in this series is 7


For the above series:-


a = 11 , n=7


A7 = 29


Using formula, An = a + (n-1)d


A7 =11 + (7-1)d = 29


6d = 29 – 11


6d = 18


d = 3


We can see from the definition that A1, A2, A3, A4 and A5 are five arithmetic mean between 11 and 29, where d = 3, a = 11


Therefore, Using formula of arithmetic mean i.e. An = a + nd


A1 = a + nd


= 11 + 3


= 14


A2 = a + nd


= 11 + (2)3


= 17


A3 = a + nd


= 11 + (3)3


= 20


A4 = a + nd


= 11 + (4)3


= 23


A5 = a + nd


= 11 + (5)3


= 26


Ans) 14, 17, 20, 23 and 26 are the required numbers.


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