Question

Find the 31st and nth terms of the series 1,-2,-5,-8,.....

Answer 1

1, -2,-5,-8

a1 = 1 a2= -2

d= a2 - a1
= -2-1
= -3

a31 = a+30d
= 1 + 30×-3
=1-90
=-89

Answer 2

$\textbf {Hey there, here is the solution.}$

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a1 = 1 (Given)

Find the difference between the terms:

d = -5 - (-2) = -3

Find the nth term:

an = a1 + (n - 1)d

an = 1 + (n - 1) (-3)

an = 1 -3n + 3

an = 4 - 3n

Find the 31st term:

a31 = 4 - 3(31)

a31 = -89

Answer: The nth term is 4 - 3n and the 31st term is -89

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⭐$\textbf {Cheers}$⭐