Question

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

Answer 1

Answer:

$T_n = 2n - 1 + T_{n-1}$

Step-by-step 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:

$T_n = 2n - 1 + T_{n-1}$