The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.
<h3>What is the nth term of an arithmetic sequence?</h3>
The general form of the nth term of an arithmetic sequence is
an = a1 + (n - 1)d
Where,
a1 - first term
n - number of terms in the sequence
d - the common difference
<h3>Calculation:</h3>
The given sequence is an arithmetic sequence.
First term a1 = = 3/2
Last term an = = 5/2
Common difference d = 1/9
From the general formula,
an = a1 + (n - 1)d
On substituting,
5/2 = 3/2 + (n - 1)1/9
⇒ (n - 1)1/9 = 5/2 - 3/2
⇒ (n - 1)1/9 = 1
⇒ n - 1 = 9
⇒ n = 9 + 1
∴ n = 10
Thus, there are 10 terms in the given arithmetic sequence.
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Disclaimer: The given question in the portal is incorrect. Here is the correct question.
Question: If the first and the last term of an arithmetic progression with a common difference are , and 1/9 respectively, how many terms has the sequence?
The value of x from the given expression is 0.7558
<h3>Solving exponential equations</h3>
The standard exponential equation is expressed as y = ab^x
Given the equation below
10^x +5 = 60
Subtract 5 from both sides
10^x = 60 - 5
10^x = 55
Take the log of both sides
log10^x = log55
x = log55/log10
x = 0.7558
Hence the value of x from the given expression is 0.7558
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Answer:
f(x) =
Step-by-step explanation:
The given options are,
a) f(x) =
b) f(x) =
c) f(x) =
d) f(x) =
Now, clearly a) is a monotonically increasing function, hence discarded, and both of c) and d) don't pass through (0, 1) hence they are also discarded.
Only b) is a decay function which does also pass through (0, 1), hence, b) is the correct option.
The value of 7 in 7,283 is 10 times the value of 7 in 2,783