Question

Can someone please help the first one is find the sum of the first 5 terms of the geometric series 7,21,63... the choices are A.91 B.280 C.847 D.2548 the second is vernas starting salary is 32,000 a year she will get a 4% raise annually how much money will she have made after 7 years? A.173,322.32 B212,255.21 C.252,745.42 D.294,855.24 and the last one which of the following is not a geometric sequence? A.1,2,4,8 B. 3,1,-1,-3 C. 9,14,19,24 D. 8,13,18,23 i did the rest of the questions but i got stuck on these three my teacher was absent and I had a sub so we didnt learn this.

Answer 1

@Lena772

Answer 2

Ok well for the first question each number in the sequence is being multiplied by 3.

They only give you the first 3 terms. 7, 21, 63.

63*3=189
189*3= 567

So those are the next two terms.

7+21+63+189+567=?

Answer 3

847?

Answer 4

Yup, C. :)

Answer 5

Money is being raised 4% each year. So 104% of the current salary is the new salary

104/100*32000=33280 (salary after first year)
104/100*33280= 34,611.20 (salary after second year)

Can you continue from here to find her salary after the seventh year?

Answer 6

yes i understand what about the last question

Answer 7

A geometric sequence is one that goes from term to term by the subtraction or addition of the same value.

Answer 8

So A would not be a geometric sequence. :)

Answer 9

oh ok i understand thanks so much oh hold on sorry one last question before you go if you dont mind

Answer 10

Sure?

Answer 11

find the s25 for 3+7+11+15+... the choices are A.1,263 B.1,267 C.1,271 D. 1,275

Answer 12

s25?

Answer 13

you mean the 25th number in the sequence?

Answer 14

yea thats what the question asked i think so it doesnt clarify

Answer 15

So each time where adding on a number that is increased by a certain value, can you see which value this is?

Answer 16

4?

Answer 17

YES!

Answer 18

Good

Answer 19

So we are finding the SUM of the first 25 numbers of the sequence.

Answer 20

3+7+11+15+19+23+27+31+35+39+43+47+51+55+59+63+67+71+75+79+83+87+91+95+99

Answer 21

Count the numbers, make sure there's 25

Answer 22

3+7+11+15+19+23+27+31+35+39+43+47+51+55+59+63+67+71+75+79+83+87+91+95+99=?

Answer 23

1257?

Answer 24

hey before we countinue for the one with the salary i keep get more than my anwser choices idk why/?

Answer 25

No, not correct.

Answer 26

I will help you with that after we get this one done.

Answer 27

okay

Answer 28

its 1275

Answer 29

sorry i flipped the last number

Answer 30

yup, D!

Answer 31

okay and about the third one i keep getting 42107?

Answer 32

104/100*32000=33280 (salary after first year)
104/100*33280= 34,611.20 (salary after second year)
104/100*34611.2=35995.65 (salary after third year)
104/100*35995.65=37435.48 (salary after fourth year)
104/100*37435.48=38932.90 (salary after fifth year)
104/100*38932.90=40490.22 (salary after sixth year)
104/100*40490.22=42109.83 (salary after seventh year)

32000+33280+34,611.20+35995.65+37435.48+38932.90 +40490.22+42109.83=?

Answer 33

oh wow okay thanks so i was doing it right i just read the number wrong thanks so much for all your help ill make sure to fan you ...

Answer 34

You did it right, you just didn't add her salaries together to see how much she made! So what is the sum of all of her salaries?

Answer 35

i got 294855.28?

Answer 36

i mean .24

Answer 37

i have to go but thank you so much for your help .

Answer 38

You're welcome, goodbye.

Answer 39

Ranga is right

Answer 40

@Lena772 and @Karina1: You can get the answers quickly if you use the standard formula for the sum of the first n terms of a geometric series and an arithmetic series:\[\text {Geometric Series:}~~a + ar + ar^2 + ar^3 + ... + ar^{n-1}\]\[\quad \quad \text {Sum = } ~ a \frac{ 1 - r^n }{ 1 - r }\]\[\text {Arithmetic Series}:~~a _{1} + (a _{1} + d) + (a _{1} + 2d) +...+ (a _{1} + (n-1)d)\]\[\quad \quad \text {Sum} = \frac{ n }{ 2 }(a _{1} + a _{n}). \quad \text { Last term } a_{n} = a_{1} + (n - 1)d\]
Verna's starting salary is 32,000 a year she will get a 4% raise annually how much money will she have made after 7 years?

The teacher's salary starts at 32000 and gets multiplied by 1.04 each year (4% raise). It is a geometric series. What is the sum after 7 years?

a = 32000; r = 1.04; n = 7;
Sum = a * (1 - r^n) / (1 - r)
= 32000(1 - 1.04^7) / (1 - 1.04) = 252,745.42

For the problem: find the S25 for 3+7+11+15+...
the choices are A.1,263 B.1,267 C.1,271 D. 1,275

It is an arithmetic progression with the first term a1 = 3, common difference d = 4 and total number of terms n = 25.
The nth term an is given by the formula: an = a1 + (n-1)d
an = 3 + (25-1)(4) = 3 + 24*4 = 99
Sum = n/2 * (a1 + an) = 25/2 * (3 + 99) = 1275. Choice D.

Which of the following is not a geometric sequence?
A.1,2,4,8 B. 3,1,-1,-3 C. 9,14,19,24 D. 8,13,18,23

A is geometric sequence because each term gets MULTIPLIED by the same number, which in this case is 2.

B is arithmetic sequence because each term DIFFERS from the previous by the same amount and in this case it is -2.

C is arithmetic sequence because each term DIFFERS from the previous by the same amount and in this case it is 5.

D is arithmetic sequence because each term DIFFERS from the previous by the same amount and in this case it is 5.

B,C,D are NOT geometric sequences. A is a geometric sequence.