Several terms of a sequence StartSet a Subscript n EndSet Subscript n equals 1 Superscript infinity are given below. {1, negative 5, 25, negative 125, 625, ...} a. Find the next two terms of the sequence. b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term of the sequence). c. Find an explicit formula for the general nth term of the sequence.

(a) -3125, 15625

(b)

(c)

Step-by-step explanation:

The sequence is given as:

(a)The next two terms of the sequence are:

625 X -5 = - 3125

-3125 X -5 =15625

(b)Recurrence Relation

The recurrence relation that generates the sequence is:

(c)Explicit Formula

The sequence is an alternating geometric sequence where:

Therefore, an explicit formula for the sequence is:

step-by-step explanation:

left be aligning the decimal points is required to not required see the number of digits to the right