Question

What is the n tern of the sequence 25, -125, 625, -3125, ... ?

Answer 1

nth term of the sequence is (-1)^(n-1) 5^(n+1)

we have to find out nth term of the sequence ; 25, -125, 625, -3125, ......

here sequence is like as 25, 25(-5), 25(-5)², 25(-5)³ ......

we know as well, sequence a, ar, ar² , ar², ar³ ....... are in geometric sequence.

nth term in GP = arⁿ-¹

where a is first term and r is common ratio of geometric progression.

25, 25(-5), 25(-5)², 25(-5)³ .......

first term, a = 25

common ratio, r = -5

so, nth term = 25(-5)^(n - 1) = (5²)(-5)^(n-1) = (-1)^(n-1) (5)^(n - 1 + 2)

= (-1)^(n-1) 5^(n+1)

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Answer 2

15625

Step-by-step explanation:

In the above sequence all the numbers are in power of 5.

25, -125, 625, -3125, ...

=$(-5)^2,(-5)^3,(-5)^4,(-5)^5,$

So the next term will be$(-5)^6$

                                       =15625