What is the explicit formula for this sequence? 2, 10, 50, 250, 1250, …
2 answers:
Answer:
Step-by-step explanation:
We have been given the sequence 2, 10, 50, 250, 1250, …
The first term is 2.
When we multiply this term by 5 then we get the second term which is 10
Similarly, When we multiply second term by 5 then we get the third term which is 50.
So, we can conclude that every time we multiply 5 to any term we'll get the next term.
In other words, we can say that the ratio of two consecutive term of this sequence is equal. And hence the sequence is a geometric sequence with common ratio r = 5
nth term of geometric sequence is given by
On substituting the known values, we get
Therefore, the explicit formula is given by
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Answer:
1)
2)
3)
Step-by-step explanation:
To evaluate or simplify expressions with exponents, we use exponent rules.
1. An exponent is only a short cut for multiplication. It simplifies how we write the expression.
2. When we multiply terms with the same bases, we add exponents.
3. When we divide terms with the same bases, we subtract exponents.
4. When we have a base to the exponent of 0, it is 1.
5. A negative exponent creates a fraction.
6. When we raise an exponent to an exponent, we multiply exponents.
7. When we have exponents with parenthesis, we apply it to everything in the parenthesis.
We will use these rules to simplify.
Problems:
1)
n^-6 has a negative exponent and should be moved to the denominator while p^0 is equal to 1
2)
Divide each base by subtracting exponents. a^4-1 = a^3 and b^-3--2=b^-1. B has a negative exponent so move it into the denominator.
3)
Simplify inside the parenthesis first by adding exponents of same bases x^-2+3 = x. Then apply the outside exponent using power to a power rule and negative exponent rule.