Insert the missing term: 3, 8, 35, 48, ?, 120

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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Let the unknown number be x

3; 8; 35; 48; x; 120

Look for a pattern

 `2^2 -1; 3^2 -1; 6^2 -1; 7^2 -1; x ; 11^2 -1`

Note the pattern has  +3 after the first two terms and , based on the sixth term being 11, we see the +3 again after the next 2

`therefore ` `T1= (n+1)^2 -1`

`T2=(n+1)^2-1`

`T3= (n+1 +2)^2 -1`

`T4= (n+1+2)^2 -1`

`T5= (n+1 +4)^2 -1`

`T6= (n+1+4)^2 -1`

I wrote down all the terms to help you see the pattern as it develops

As we are looking for T5 = x

 `T5 = x= (n+1+4)^2 -1`  as n=5 substitute:

`x= (5 + 1+4)^2 -1`

`x= (10)^2 -1`

`therefore` x= 99. The missing term is 99

 

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