All categories

3 years ago

Please help me. Given the explicit formula for an arithmetic sequence find the 52nd term.

Mathematics

1 answer:

ivann1987 [24]3 years ago

3 0

Answer:

a = -41 +30n

52nd term is

a52 = -41 + 30(52)

a52 = -41 + 1560

a52 = 1519

You might be interested in

An English teacher has 6 short stories, 4 novels, and 23 poems to choose from. How many ways can he assign one of each to his cl

Karolina [17]

Answer:

552

Step-by-step explanation:

This is a problem of permutation which can be solved by rule of fundamental counting principle.

This principle states that if there "m" ways of doing one thing and "n" ways of doing other. Then no. of ways in which both the things can be done together is "m*n". This can be extended for m, n, p,r, s things and so on.

example: if there are 5 shirts and 3 trousers then number of ways in which the shirts and trousers can be worn is 5*3 = 15 ways.

_____________________________________________

The given problem is on similar concepts.

here 6 short stories, 4 novels, and 23 poems have to be assigned to his class.

Thus it can be done in 6*4*23 = 552 ways.

5 0

3 years ago

1. What are the first five terms of the sequence given by the formula an = 5n + 1?

Dvinal [7]

The correct answers are:

(1) 6, 11, 16, 21, 26 (Option B)

(2) $~a_1 = 8$ ; $~a_n = a_{n-1} - 2~$ (Option A)

(3) $~a_n = -2 + 3(n-1)~~~~$ (Option D)

Explanations:

(1) Given Sequence:

$a_n = 5n + 1$

Now in order to find the first 5 terms, we need to put n=1,2,3,4,5 in the above sequence and solve.

For n=1: $a_1 = 5(1) + 1 = 6$

For n=2: $a_2 = 5(2) + 1 = 11$

For n=3: $a_3 = 5(3) + 1 = 16$

For n=4: $a_4 = 5(4) + 1 = 21$

For n=5: $a_5 = 5(5) + 1 = 26$

Hence, the first five terms are: 6, 11, 16, 21, 26 (Option B)

(2) Given Sequence:

8, 6, 4, 2, …

Now to find the recursive definition, we need to adopt trial-and-error approach.

As, $a_1 = 8$ (meaning the first element of the sequence is 8), the second or nth value of the sequence can be found by using the following formula:

$a_n = a_{n-1} - d$ --- (1)

Where, n = the index of the number in a sequence

d = difference between two consecutive numbers = 8-6 = 2

Now,

The second number of the sequence has to be 6 by using (1). Put n = 2 and d = 2 in (1):

$a_2 = a_{2-1} - 2$

$a_2 = a_{1} - 2$

Since $a_1 = 8$ , therefore,

$a_2 = 8 - 2 = 6$ (correct)

Hence the correct answer is $a_1 = 8$ ; $~a_n = a_{n-1} - 2~$ (Option A)

(3) Given Sequence:

−2, 1, 4, 7, …

To find the explicit definition, use the following formula:

$a_n = a_1 + (n-1)*d$ --- (X)

Where,

$a_n = nth~term~of~the~sequence \\a_1 = 1st~term~of~the~sequence = -2 \\d = common~difference = 4-1 = 7-4 = 3 \\n = index~of~a~number~in~a~sequence \\$