Find the exact value (either decimal or fractional form) of the first term of an arithmetic sequence if the sum of the first 100 terms is 7099.5 and the sum of the next 100 terms is 20799.
 👍
 👎
 👁
 ℹ️
 🚩
2 answers

We find a from a system:
a +a+99d =7099.5
a+100d+a+199d=20799
We subtract from the 2nd the 1st:
200d=13699.5
d=68.4975
2a+99x68.4975=7099.5
a=159.12375 (0.12375=99/800) 👍
 👎
 ℹ️
 🚩
answered by Mgraph 
Ummm.
Sn = n(a1 + an)/2
S100 = 100(a1 + a100)/2
= 50(a+a+99d)
= 100a + 4950 👍
 👎
 ℹ️
 🚩
answered by Steve
Answer this Question
Related Questions

PreCalc
The fifth term of an arithmetic sequence is equal to 6 and the sum of the first 12 terms is equal to 45. Find the first term and the common difference. having trouble with this, can't figure out the steps?
 asked by jeff

Math
Penn writes a 2013term arithmetic sequence of positive integers, and Teller writes a different 2013term arithmetic sequence of integers. Teller's first term is the negative of Penn's first term. Each then finds the sum of terms in his sequence. If their
 asked by Matt

Maths
1) In the arithmetic progression, the 8th term is twice the 4th term and the 20th term is 40. Find the common difference and the sum of the terms from the 8th to the 20th term inclusive. 2) Find the least number of terms of the AP, 1+3+5...that are
 asked by Anonymous

Math
 If the 4th term of an arithmetic sequence is 24 and the 12th term is 56, whats the first term?
 asked by Samantha Silva

math
Determine whether each sequence is arithmetic or geometric. Find the next three terms. 1. 14, 19, 24, 29, . . . (1 point) geometric, 34, 39, 44 arithmetic, 32, 36, 41 arithmetic, 34, 39, 44 *** The sequence is neither geometric nor arithmetic. 2. –4, 8,
 asked by TTR+S<3

c$s college
the first term of an arithmetic progression is 3 and the fifth term is is 9.find the number of terms in the progression if the last term is 81
 asked by Umaru Monsurat

Mathematics : Arithmetic Sequence
The 5th term and the 8th term of an arithmetic sequence are 18 and 27 respctively. a)Find the 1st term and the common difference of the arithmetic sequence. b)Find the general term of the arithmetic sequence.
 asked by Charmian

Algebra
Determine whether each sequence is arithmetic or geometric. Find the next three terms. 14, 19, 24, 29, . . . A.geometric, 34, 39, 44 B.arithmetic, 32, 36, 41 C.arithmetic, 34, 39, 44 D.The sequence is neither geometric nor arithmetic. I think this is C...?
 asked by Cassie

Math
The first term and last term of an arithmetic progression are 3 and 145 respectively .if the common difference is 4.(a) find the 12th term (b) find the 25th term.
 asked by Tolu

Urgent math
how do I do this can any body show me how? An arithmetic sequence begins 4, 9, 14, 19, 24, . . . . (a) Find the common difference d for this sequence. d = (b) Find a formula for the nth term an of the sequence. an = (c) Find the 35th term of the sequence.
 asked by Aileen

math
what are the similarities and differences between an arithmetic sequence and a linear equation? ok i know that arithmetic sequence is a sequence of real numbers for which each term is the previous term plus a constant (called the common difference). For
 asked by Claudia

Math
Find the 10th term of a nonconstant arithmetic sequence whose 1st term is 3 with the 1st, 4th, and 13th term forming a geometric sequence. I've tried doing it differently everytime, but I always come to a dead end..
 asked by Anon

Math/Precal
what is the first term of an arithmetic sequence if the 7th term is 21 and the 10th term is 126
 asked by Nancy

mathematics
1.1 the third term of an arithmetic sequence is 8 and the 15 term is 44 . Calculate: 1.1 the common difference and first term. 1.2 the sum of the first 50 terms. 1.2 1;4;7;10.... Is an arithmetic sequence .find: 1.2.1 the 30 term.
 asked by tankiso

math
find the 4th term of an arithmetic sequence whose first term is 8 and whose 9th term is 32.
 asked by breauna

math
The 3rd term of an Arithmetic Progression is 10 more than the first term while the fifth term is 15 more than the second term. Find the sum of the 8th and 15th terms of the Arithmetic Progression if the 7th term is seven times the first term.
 asked by Toba

Math
1. What is the tenth term of the geometric sequence whose first term (a1) is 16 and the common ratio (r) is –½? 2. Given the terms a10 = 3 / 512 and a15 = 3 / 16384 of a geometric sequence, find the exact value of the first term of the sequence.
 asked by Jade

arithmetic
Find the sum of the 25th term to 50th term of the arithmetic progression 28,23,18, ...
 asked by Eryea

math
I can't solve this one: The second term of an arithmetic sequence is 24 and the fifth term is 3.Find the first term and the common difference. How could I get the answers if there's only two given numbers?
 asked by maiah

arithmetic progression
four positive integers form an arithmetic progression . if the product of the first and the last terms is 70 and the second and third terms are 88, find the first term
 asked by Superstix
Still need help?
You can ask a new question or browse existing questions.