texelaare

2021-08-15

Arithmetic Sequence? Find the first five terms of the sequence, and determine whether it is arithmetic. If it is arithmetic, find the common difference, and express the nth term of the sequence in the standard form ${a}_{n}=a+(n-1)d$

$a}_{n}=4+{2}^{n$

liannemdh

Skilled2021-08-16Added 106 answers

To find:

The first five terms of the sequence, and check whether it is arithmetic sequence or not. If it is arithmetic sequence, find the common difference, and express the nth term of the sequence in the standard form${a}_{n}=a+(n-1)d$

Concept used:

The difference between the successive terms of an arithmetic sequence is constant.

Calculation:

Given sequence is,

$a}_{n}=4+{2}^{n$ .......(1)

Substitute 1 for n in equation (1) to calculate the first term of this sequence.

$a}_{1}=4+{2}^{1$

$=4+2$

$=6$

Substitute 2 for n in equation (1) to calculate the second term of this sequence.

$a}_{2}=4+{2}^{2$

$=4+4$

$=8$

Substitute 3 for n equation (1) to calculate the third term of this sequence.

$a}_{3}=4+{2}^{3$

$=4+8$

$=12$

Substitute 4 for n equation (1) to calculate the fourth term of this sequence.

$a}_{4}=4+{2}^{4$

$=4+16$

$=20$

Substitute 5 for n equation (1) to calculate the fifth term of this sequence.

$a}_{5}=4+{2}^{5$

$=4+32$

$=36$

Difference between first and second term can be calculated as,

${a}_{2}-{a}_{1}=8-6$

$=2$

Difference between second and third term can be calculated as,

${a}_{3}-{a}_{2}=12-8$

$=4$

Since, the difference between the successive terms of the given sequence is not constant.

Therefore, the sequence$a}_{n}=4+{2}^{n$ is not arithmetic.

Conclusion:

Hence, the sequence$a}_{n}=4+{2}^{n$ is not arithmetic.

The first five terms of the sequence, and check whether it is arithmetic sequence or not. If it is arithmetic sequence, find the common difference, and express the nth term of the sequence in the standard form

Concept used:

The difference between the successive terms of an arithmetic sequence is constant.

Calculation:

Given sequence is,

Substitute 1 for n in equation (1) to calculate the first term of this sequence.

Substitute 2 for n in equation (1) to calculate the second term of this sequence.

Substitute 3 for n equation (1) to calculate the third term of this sequence.

Substitute 4 for n equation (1) to calculate the fourth term of this sequence.

Substitute 5 for n equation (1) to calculate the fifth term of this sequence.

Difference between first and second term can be calculated as,

Difference between second and third term can be calculated as,

Since, the difference between the successive terms of the given sequence is not constant.

Therefore, the sequence

Conclusion:

Hence, the sequence

Jeffrey Jordon

Expert2022-07-07Added 2605 answers

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

Which operation could we perform in order to find the number of milliseconds in a year??

$60\cdot 60\cdot 24\cdot 7\cdot 365$ $1000\cdot 60\cdot 60\cdot 24\cdot 365$ $24\cdot 60\cdot 100\cdot 7\cdot 52$ $1000\cdot 60\cdot 24\cdot 7\cdot 52?$ Tell about the meaning of Sxx and Sxy in simple linear regression,, especially the meaning of those formulas

Is the number 7356 divisible by 12? Also find the remainder.

A) No

B) 0

C) Yes

D) 6What is a positive integer?

Determine the value of k if the remainder is 3 given $({x}^{3}+k{x}^{2}+x+5)\xf7(x+2)$

Is $41$ a prime number?

What is the square root of $98$?

Is the sum of two prime numbers is always even?

149600000000 is equal to

A)$1.496\times {10}^{11}$

B)$1.496\times {10}^{10}$

C)$1.496\times {10}^{12}$

D)$1.496\times {10}^{8}$Find the value of$\mathrm{log}1$ to the base $3$ ?

What is the square root of 3 divided by 2 .

write $\sqrt[5]{{\left(7x\right)}^{4}}$ as an equivalent expression using a fractional exponent.

simplify $\sqrt{125n}$

What is the square root of $\frac{144}{169}$