Question

Find the nth term for the following question: -5,-2,3,10,19​

Answer 1

`T_n = 2n - 1 + T_(n-1)`

Explanation:

Given

`Sequence: -5,-2,3,10,19`

Required

Find the nth term

We have:

`T_1 = -5`

`T_2 = -2 = 3 - 5 = 3 + T_1`

`T_3 = 3 = 5 - 2 = 5 + T_2`

`T_4 = 10 = 7 + 3 = 7 +T_3`

`T_5 = 19 = 9 + 10 = 9 + T_4`

This gives:

`T_2 = 3 + T_1 = 4 - 1 + T_1`

`T_3 = 5 + T_2 = 6 - 1 + T_2`

`T_4 = 7 +T_3 = 8 - 1 + T_3`

`T_5 = 9 + T_4 = 10 - 1 + T_4`

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Solving further, we have:

`T_2 = 4 - 1 + T_1 = 2 * 2 - 1 + T_1`

`T_3 = 6 - 1 + T_2 = 2 * 3 + T_2`

`T_4 = 8 - 1 + T_3 = 2 * 4 - 1 + T_3`

`T_5 = 10 - 1 + T_4 = 2 * 5 - 1 + T_4`

Following the above sequence: the nth term is:

`T_n = 2n - 1 + T_(n-1)`