SOLUTION: Find sum of 9 terms in a
arithmetic sequence is 207 sum of first 20 terms
is 900 . Find fifth and twenty fifth term Find
the sum of 100 terms
Algebra.Com
Question 1042037: Find sum of 9 terms in a
arithmetic sequence is 207 sum of first 20 terms
is 900 . Find fifth and twenty fifth term Find
the sum of 100 terms
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If the sum of 9 terms in an arithmetic sequence is 207 and the sum of first 20 terms is 900 ,
Find fifth and twenty-fifth term
--------
S(9) = (a(1)+(a(1)+8d)*(9/2) = 207
S(20) = (a(1)+(a(1)+19d)*(20/2) = 900
--------
2(a(1)) + 8d = (2/9)207 = 2*23 = 46
2(a(1)) + 19d = 90
------
Subtract and solve for "d"::
11d = 44
d = 4
----
Then, solve for a(1)::
2*a(1) + 8d = 46
2*a(1) + 32 = 46
a(1) = 7
------------------------
Ans: a(5) = 7 + 4d = 7 + 16 = 23
a(25) = 7 + 24d = 7 + 96 = 103
----------------------------
Find the sum of 100 terms.
s(100) = (7 + a(100))*(50)
a(100) = 7 + 99*4 = 403
S(100) = 410*50 = 20500
-------------
Cheers,
Stan H.
---------------
RELATED QUESTIONS
The first difference of a sequence is the arithmetic sequence 3, 5, 7, 9, 11, ...... Find (answered by greenestamps,ikleyn)
the fifth term of a geometric sequence is 252 and the common ratio is 0.5 find the first... (answered by josgarithmetic,MathTherapy)
Find the sum of the first twenty terms of the arithmetic sequence given that the tenth... (answered by Fombitz)
An arithmetic and geometric series both have the same first terms,a=9. The fifth term of... (answered by ikleyn)
THE FIFTH TERM OF AN ARITHEMETIC SEQUENCE IS 10 & THE SUM OF THE THE FIRST 10 TERMS IS... (answered by pakhi)
if the first, fifth and tenth terms of an arithmetic sequence are in geometric... (answered by KMST)
The tenth term of an arithmetic sequence is 20 and the fifth term is 0. Find the sum of... (answered by Fombitz)
The fifth term of an arithmetic progression is 24 and the sum of the first tenth terms is (answered by josgarithmetic)
The seventh term of a geometric sequence is twice the fifth term and the sum of the first (answered by ikleyn)