Question

You are given a sequence of thirteen terms, each an integer, such that the fourth term is 17 and the eighth term is 29. You are also given that the sum of any three consecutive terms in the sequence is the same and that the sum of the thirteen terms is 217. What is the sequence? Someone pllzzzz help

Answer 1

Explanation:

Let the sequence as :

`T_1, T_2, T_3, 17, T_5, T_6,......T_(13)`

I put 17 there as
`T_4` because I want 3 consecutive elements. Let A is the sum of them.

`T_1+T_2+T_3 = A`

17

`T_5+T_6+T_7 = A`

`T_8+T_9+T_(10) = A`

`T_(11)+T_(12)+T_(13)=A`

`\sum T_i + 17 = 217 = 4A + 17`

Hence A = 50

Then, back to the condition

`T_4+ T_5 + T_6 = A = 50`

`T_5+T_6+T_7 = A = 50`

Subtract them, we get

`T_4 - T_7 = 0`

That gives you

`T_4 = T_7 = 17`

Do the same with other groups.