sequences question

Original post by SunDun111

the question is, The first term of a arithmetic sequence is six times the 5th term and the sum of the 2nd and 8th term is 8, find the 20th term of this sequence.

Im kinda confused, I know i need to find A and D and can get a one of the simultaneus equations, but the 2nd one reguarding the sum of the 2nd and 8th term is is confusing to make a simultaneus equation?

2nd term is A + d

8th term is A + 7d

Sum of 2nd and 8th term is A + d + A + 7d = 8

Reply 2

the bear

20

and the 5th term is A + 4d ?

Reply 3

OP

Original post by Zacken

2nd term is A + d

8th term is A + 7d

Sum of 2nd and 8th term is A + d + A + 7d = 8

Original post by SunDun111

the question is, The first term of a arithmetic sequence is six times the 5th term and the sum of the 2nd and 8th term is 8, find the 20th term of this sequence.

Im kinda confused, I know i need to find A and D and can get a one of the simultaneus equations, but the 2nd one reguarding the sum of the 2nd and 8th term is is confusing to make a simultaneus equation?

thanks guys

Reply 4

OP

Original post by the bear

and the 5th term is A + 4d ?

i already worked out the equation, got the answer right but the 5th term is

5A + 24D = 0 when you figure out properly

Reply 5

Original post by SunDun111

thanks guys

No problem.

Reply 6

OP

Original post by Zacken

No problem.

came acorss another question, it is The sum of the first 30 terms of an arthimetic series is 90, The sum of the next 10 terms is also 90, Find the first 1st term and common difference,

i thought i'd use the sum formula, and got
1/2 multiplied by 30 (2a + 29d) = 90
and my second one would be

1/2 multiplied by 40(2a + 39d) = 90
i cant get the right answer have i made my equations wrong

Reply 7

Original post by SunDun111

1/2 multiplied by 40(2a + 39d) = 90
i cant get the right answer have i made my equations wrong

Yes, this bit is wrong. It says the sum of the next 10 terms is 90.

That is, the 31st + 32nd + 33rd + ... + 40th term is 90.

i.e: A + 30d + A + 31d + A + 32d + ... + A + 39d = 10A + 345d = 90.

Reply 8

OP

Original post by Zacken

Yes, this bit is wrong. It says the sum of the next 10 terms is 90.

That is, the 31st + 32nd + 33rd + ... + 40th term is 90.

i.e: A + 30d + A + 31d + A + 32d + ... + A + 39d = 10A + 345d = 90.

Original post by Zacken

Yes, this bit is wrong. It says the sum of the next 10 terms is 90.

That is, the 31st + 32nd + 33rd + ... + 40th term is 90.

i.e: A + 30d + A + 31d + A + 32d + ... + A + 39d = 10A + 345d = 90.

not really following here, wouldnt it be 0.5 x 10 ( 2a + 9D ) = 90?

Reply 9

Original post by SunDun111

not really following here, wouldnt it be 0.5 x 10 ( 2a + 9D ) = 90?

No, that's the first 10 terms.

Reply 10

OP

Original post by Zacken

No, that's the first 10 terms.

yeah but from the 30th to 40th they is 10 terms, so wouldnt it still be 0.5 multipled by 10? even though your right what im kinda confused about how you got the second equation

Reply 11

Original post by SunDun111

yeah but from the 30th to 40th they is 10 terms, so wouldnt it still be 0.5 multipled by 10? even though your right what im kinda confused about how you got the second equation

No. Your formula only works if it is the first ten terms. Not any random set of ten terms.

My equation is just:
31st term: A + 30d
32nd term: A + 31d
.
.
.
40th term: A + 39d

So add them all up:
A + 30d + A + 31d + ... + A + 39d
That's 10A + 345d

(edited 8 years ago)

Reply 12

OP

Original post by Zacken

No. Your formula only works if it is the first ten terms. Not any random set of ten terms.

My equation is just:
31st term: A + 30d
32nd term: A + 31d
.
.
.
40th term: A + 39d

So add them all up:
A + 30d + A + 31d + ... + A + 39d
That's 10A + 345d

Ok thanks i understand

Reply 13