More Arithmetic Problems

[SabziiKumari]

hi
i have already recieved excellent help on one questions but i have 2 others that i need help on . thanks!

1) The 5th term of an arithmetic series is 7
common difference is 4.
find the first term and the sum of the first 10 positive terms.

2) the sum of the first n terms of a series is n(n+2) . find the first three terms of the series.

 

[Deleted member 4993]

hi
i have already recieved excellent help on one questions but i have 2 others that i need help on . thanks!

1) The 5th term of an arithmetic series is 7
common difference is 4.
find the first term and the sum of the first 10 positive terms.

\(\displaystyle a_n = a_1 + (n-1) * d\)

The equation above will give you the first term of the series.

Now continue...
2) the sum of the first n terms of a series is n(n+2) . find the first three terms of the series.

You have posted 3 problems - without a line of work.

You have been given extensive help on the first problem. Use those concepts and show us what you are thinking.

Please share your work/thought with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[SabziiKumari]

1)
i did manage to work out the first term which was -9

to get this i did : a + 4d = 7 --> a +16=7 --> a=-9
common difference was 4

the sum of the first 10 positive terms
i know that a = -9 and d=4 . would n =10 ?

when i worked it out using the sum of series formula
i got the answer 90 but this is incorrect as the answer should be 210. but i dont know how you get that.

question 2) . i have no idea where to start in answering it.
thanks

 

[Denis]

the sum of the first 10 positive terms
i know that a = -9 and d=4 . would n =10 ?

Read carefully: first 10 POSITIVE terms; -9, -5 and -1 are negative terms:
so 1st term of the 10 positive terms is 3 ; kapish?

 

[Deleted member 4993]

1)
i did manage to work out the first term which was -9

to get this i did : a + 4d = 7 --> a +16=7 --> a=-9
common difference was 4

the sum of the first 10 positive terms
i know that a = -9 and d=4 . would n =10 ?

Your series is

-9, -5, -1, 3, 7, 11,.....

The positive numbers start with 3 - and you got sum 10 numbers from there.

when i worked it out using the sum of series formula
i got the answer 90 but this is incorrect as the answer should be 210. but i dont know how you get that.

question 2) . i have no idea where to start in answering it.
thanks

 

[Denis]

question 2) . i have no idea where to start in answering it.

"2) the sum of the first n terms of a series is n(n+2) . find the first three terms of the series."

If n = 1, n(n+2) = 3
If n = 2, n(n+2) = 8
If n = 3, n(n+2) = 15 ; those are the "SUMS"

So what are the terms?

 

[SabziiKumari]

thank for question 1
i actually had taken some time out to work it out.
so thanks for not telling me straight away as with a little thought i managed to figure it out.


question 2 :

If n = 1, n(n+2) = 3
If n = 2, n(n+2) = 8
If n = 3, n(n+2) = 15 ; those are the "SUMS"

if those are the sums , i don't know what i would do next.
would i put them into the sum of series equation.

 

[Denis]

question 2 :

If n = 1, n(n+2) = 3
If n = 2, n(n+2) = 8
If n = 3, n(n+2) = 15 ; those are the "SUMS"

if those are the sums , i don't know what i would do next.
would i put them into the sum of series equation.

3 + ? = 8
8 + ? = 15

 

[SabziiKumari]

right
so the answer would be 3,5,7 ?
if you started with n=0
but could you please explain how you came about adding
3+ ? =8
8 + = 15

thanks

 

[Denis]

series: 3,5,7,9,11 .....
sums: 3,8,15,24,35 ....
sum of 1st n terms when n=1 is simply the 1st term!