SOLUTION: In an arithmetic progression, the 3rd term is equal to three times the 1st term, and the sum of the first two terms is equal to 3.
find the nth term of this series.
Hence find th
Algebra.Com
Question 754592: In an arithmetic progression, the 3rd term is equal to three times the 1st term, and the sum of the first two terms is equal to 3.
find the nth term of this series.
Hence find the sum of the terms from the 1st to the nth term inclusive.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In an arithmetic progression,
the 3rd term is equal to three times the 1st term, and the sum of the first two terms is equal to 3.
find the nth term of this series.
------
General arithmetic series term:
a(n) = a(1) +(n-1)d
-------------------------
Therefore a(3) = a(1) + 2d
------
Equation:
From the statement of the problem,
a(1) + 2d = 3*a(1)
2a(1) = 2d
a(1) = d
---------------------
From the statement of the problem,
Equation:
a(1) + a(2) = 3
a(2) = 3-d
Hence find the sum of the terms from the 1st to the nth term inclusive.
1st term: d
2nd term: 3-d
3rd term: 3-d + (3-2d) = 6-3d = 3(2-d)
4th term: 6-3d + (3-2d) = 9-5d
etc.
----
S(n) = (n/2)(a(1)+a(n)) = (n/2)(d+(d+(n-1)d)) = (n/2)((n+1)d)
=================
Cheers,
Stan H.
=================
RELATED QUESTIONS
A geometric progression has 6 terms. The first term is 192 and the common
ratio is 1.5.... (answered by greenestamps)
A geometric progression has six terms. The first term is 486 and the common ratio is ;.... (answered by greenestamps)
In an arithmetic progression, the sum of the first ten terms is 50 and the 5th term is... (answered by MathTherapy)
In an arithmetic progression, the sum of the first ten terms is 50 and the 5th term is... (answered by MathLover1,MathTherapy)
In an arithmetic series, the 3rd term is equal to 114 and the last term is equal to -27.... (answered by greenestamps)
the 5th term in a geometric progression is 9 times the 3rd term and the sum of the 6th... (answered by Boreal,ikleyn)
the 3rd and 7th term of an arithmetic progression are 18 and 30 respectively, the sum of... (answered by greenestamps)
The 3rd term of an arithmetic sequence is 24 times less than term 7,the sum of term 5 and (answered by richwmiller)
In an arithmetic progression, 8th term is 8 and sum of the first 16 terms is 144. Find... (answered by josgarithmetic)