SOLUTION: a). In an AP, the first term -5 and the last term is 105. If the sum of these terms is 1550, how many terms are there in the AP? b). The first three terms of a G.P are x+1, x+3 an

Algebra.Com
Question 1126795: a). In an AP, the first term -5 and the last term is 105. If the sum of these terms is 1550, how many terms are there in the AP?
b). The first three terms of a G.P are x+1, x+3 and x+8, and find
i) The value of x
ii) The common ratio
iii) The sum of the first 15 terms.
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
The sum of the first n terms of an arithmetic progression (of any arithmetic progression) is


 = .


This formula ideally suits to solve the given problem, since the terms   and    are given in the condition.


So, in your case


1550 =  =  = 50n,


which gives you the number of the terms  n =  = 31.


Answer.  There are  31  terms in the given AP.

---------------------

There is a bunch of lessons on arithmetic progressions in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions
    - Math Olimpiad level problem on arithmetic progression
    - Mathematical induction and arithmetic progressions
    - Mathematical induction for sequences other than arithmetic or geometric

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.


==================


Regarding your second problem in the post, there is  A  GOLDEN  RULE  in this forum,  which is the policy
and the requirement in the same time:

    ONE and ONLY ONE problem per post
RELATED QUESTIONS

1) Given that for an AP seventh term=43 and second term=91,find the valves of a,d and... (answered by richwmiller)
In an AP consisting of 15 terms, the sum of the last five terms is 305. If the sixth term (answered by ikleyn)
How many terms are there in a geometric sequence if 6 is the first term, 1/2 is the... (answered by reviewermath)
The sum of the terms of a finite arithmetic series is 624. If the sum of the 1st term... (answered by robertb)
The first and last terms of an AP are 67 and 171 respectively. If The first and last... (answered by Theo)
Find the number of terms in an A.P, whose first term is 1, last term is 77 and the sum of (answered by math_tutor2020)
The first two terms of an arithmetic sequnce are 3, 7 and the last term is 355. a. How (answered by ikleyn,josgarithmetic)
The first and last term if an AP are -0.5 and 140.5, respectively. (Q1) If the number... (answered by ikleyn)
The first term of an AP is 3. Given that the sum of the first 6 terms is 48 and that the... (answered by greenestamps,ikleyn,MathTherapy)