Question

Use the given information below to find the first 6 terms of a sequence. *

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1. -7, -19, -43, -91, -187, -379,...
2. -1, -7, -19, -43, -91, -187,...
3. -1, -6, -11, -16, -21,...
4, -6, -11, -16, -21, -26,...

Answer 1

2. -1, -7, -19, -43, -91, -187,...

Explanation:

`\purple{ \bold{a_1 = - 1}}...(given) \\ a_n = 2a_(n - 1) - 5 \\ a_2 = 2a_(1) - 5 = 2( - 1) - 5 = - 2 - 5 = \\ \purple{ \bold{a_2 = - 7}} \\ \\ a_3 = 2a_(2) - 5 = 2( - 7) - 5 = - 14 - 5 \\ \purple{ \bold{a_3 = - 19}} \\ \\ a_4 = 2a_(3) - 5 = 2( - 19) - 5 = - 38 - 5 \\ \purple{ \bold{a_4 = - 43}}\\ \\ a_5 = 2a_(4) - 5 = 2( - 43) - 5 = - 86 - 5 \\ \purple{ \bold{ a_5 = - 91}}\\ \\ a_6 = 2a_(5) - 5 = 2( - 91) - 5 = - 182- 5 \\ \purple{ \bold{a_6 = - 187}}\\`

Hence, first six terms of the given sequence are -1, -7, -19, -43, -91, -187,...