SOLUTION: yes! i need help with this problem the sum of two consecutive terms in the arithmetic sequence 1,4,7,10,,, is 299 find these two terms? thank you!

Question 354971: yes! i need help with this problem the sum of two consecutive terms in the arithmetic sequence 1,4,7,10,,, is 299 find these two terms? thank you!
Found 3 solutions by stanbon, robertb, jrfrunner:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The sum of two consecutive terms in the arithmetic
sequence 1,4,7,10,,, is 299 find these two terms?
----
a(1) = 1
d = 4-1 = 3
-------
Two consecutive terms would be:
a(n) = a(1)+(n-1)d
a(n+1) = a(1)+(n)d
-----
Equation:
1 + (n-1)3 + 1+3n = 299
---
2 + 3n-3 + 3n = 299
6n = 300
n = 50
n+1 = 51
-----
a(50) = 1 + 49*3 = 148
a(51) = 148+3 = 151
----
Check:
148+151 = 299
======================
cheers,
Stan H.
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!

asubn = asub1 + (n-1)d
asub(n+1) = asub1 + nd.
Adding corresponding sides,
asubn + asub(n+1) = 2asub1 + (2n-1)d.
then
299 = 2asub1 + (2n-1)d
299 = 2*(1) + (2n-1)*3
299 = 2 + (2n-1)3
297 = (2n-1)3
99 = 2n-1
100 = 2n
n = 50.
so its the 50th term (148) and the 51st term (151).
Answer by jrfrunner(365)   (Show Source): You can put this solution on YOUR website!
since the difference between any two numbers is constant, that defines this sequence as arithmetic.
--
The term is defined as
where (ie the first term and =difference between consecutive terms in this sequence
---
so...
---
sum of two consecutive terms:
therefore
3n-2+3n+3-2=299
6n-1=299
6n=300
n=50
--
=3*(50)-2=148
--

==
validate
148+151=299

RELATED QUESTIONS
The sum of two consecutive terms in the arithmetic sequence 1, 4, 7, 10, ... is 299. Find (answered by scott8148)
Can someone assist me with the following problem please? Use the arithmetic sequence of... (answered by jim_thompson5910)
Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,�to find the following: a) What is (answered by jim_thompson5910)
1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10� to find the... (answered by jim_thompson5910)
Anyone have any ideas what this stuff is talking about? I'm lost, I need helppppp.... (answered by venugopalramana)
i really need help with this! i already got on tutor.com and didnt understand how they... (answered by ewatrrr)
This is a long one I know, can someone please help me with this one? Use the... (answered by jim_thompson5910)
1. Use the arithmetic sequence of numbers 1,3,5,7,9,....to find the following: a.... (answered by jim_thompson5910)
Please help me solve the following problems. I've tried to solve the problem but I don't (answered by venugopalramana)