The first term of an arithmetic sequence is 5. if the25th term is 101 find the common difference?

2 answers:

8 0

An arithmetic sequence is one where each term is a constant difference, called the common difference, from the preceding term. The arithmetic sequence can always be expressed as:

a(n)=a+d(n-1), a=first term, d=common difference, n=term number.

We are given two terms and term numbers, so we can solve for the common difference...

101=5+d(25-1)

101=5+25d-d

101=5+24d

96=24d

d=4

So the common difference is 4.

horrorfan [7]3 years ago

5 0

First term a1 = 5

25th term = a1 + 24d = 101 (where d = common difference)

5 + 24d = 101
24d = 96
d = 96/24 = 4

common difference = 4

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There are 100 bacteria in a jar. Every day, the number of bacteria increases 25%. In approximately how many days will there be 5

algol [13]

Use compound interest formula

$\\ \rm\Rrightarrow P(1+r/100)^t=500$

$\\ \rm\Rrightarrow 100(1+0.25)^t=500$

$\\ \rm\Rrightarrow (1.25)^t=5$

$\\ \rm\Rrightarrow log(1.25)^t=log5$

$\\ \rm\Rrightarrow tlog1.25=log5$

$\\ \rm\Rrightarrow t(0.097)=0.3$

$\\ \rm\Rrightarrow t=3.3\approx 3$

Option A

5 0

2 years ago

Read 2 more answers

Plz help if you can Thank ya

koban [17]

Answer:

$90\pi$

Step-by-step explanation:

The first step is to find the slant height of the cone. Using the pythagorean theorem, you can find that $\sqrt{12^2+5^2}=13$ cm. Plugging this into the equation, you get $\pi \cdot 5 \cdot 13=90\pi$ . Hope this helps!