Find the next two terms in the given sequence, then write it in recursive form. A.) {7,12,17,22,27,...} B.) { 3,7,15,31,63,...}
iren [92.7K]
Answer:
A) a_n = 5n + 2
B) a_n = (2^(n + 1)) - 1
Step-by-step explanation:
A) The sequence is given as;
{7,12,17,22,27,...}
The differences are:
5,5,5,5.
This is an arithmetic sequence following the formula;
a_n = a_1 + (n - 1)d
d is 5
Thus;
a_n = a_1 + (n - 1)5
Now, a_1 = 7. Thus;
a_n = 7 + 5n - 5
a_n = 5n + 2
B) The sequence is given as;
{ 3,7,15,31,63,...}
Now, let's write out the differences of this sequence:
Differences are:
4, 8, 16, 32
This shows that it is a geometric sequence with a common ratio of 2.
In the given sequence, a_1 = 3 and a_2 = 7 and a_3 = 15
Thus, a_2 = 2a_1 + 1
Also, a_(2 + 1) = 2a_2 + 1
Combining both equations, we can deduce that: a_(n + 1) = 2a_n + 1
Thus; a_n can be expressed as:
a_n = (2^(n + 1)) - 1
The amount Sheila deposits in the Bank of US saving account is $511.
Sabrina has a total of $3,066 she wants to deposit. She has three banks that she wants to deposit her money in.
Let, a represent the amount she would deposit she would invest 7/4 bank.
The amount invested in Catch bank = 6 x a = 6a
The amount invested in Bank of US = 20% x ( 6a + a)
= 0.2 x 7a
= 1.4a
The total amount invested in the three banks can be represented with this equation:
1.4a + a + 6a = 3066
In order to determine the amount she would save in the Bank of US, the amount deposited in 7/4 bank has to be determined first.
8.4a = 3066
a = $365
The amount deposited in the Bank of US = 1.4a
= 1.4 x 365
= $511
A similar question was answered here: brainly.com/question/2289204?referrer=searchResults
Answer: 544?
Step-by-step explanation:
This is the answer if I'm supposed to solve the question in yellow
1/2*16(48+20) = 1/2*16*(68)
1/2*16=8
8*68 = 544
Could I see a picture of what kind of triangle it is please?
