The 20th term of the given sequence is 1572864
What is geometric progression?
a series of numbers in which each is multiplied or divided by a fixed number to produce the next.
According to the question
That is geometric sequence where first term a1 = - 2 and common ratio (r )= - 2
The Formula of [tex]n^{th}[/tex] term of a geometric sequence:
an = a1 ∙ r ⁿ ⁻¹
In this case:
a20 =( - 3) × ( - 2 ) ²⁰ ⁻¹
= (- 3 ) ×( - 2 ) ¹⁹
= (- 3) × ( - 1 ×2 ) ¹⁹ =
= (- 3) × ( - 1 ) ¹⁹ × ( 2 ) ¹⁹
= (- 3 )× ( - 1 ) × ( 2 ) ¹⁹
= 3 × 524288
= 1572864
Hence, the 20th term of the given sequence is 1572864
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