Questions on Algebra: Sequences of numbers, series and how to sum them answered by real tutors!

Tutors Answer Your Questions about Sequences-and-series (FREE)

Question 434295: write the next term in the sequence. then write a rule for the nth term..

-5, 10, -15, 20, ?
Click here to see answer by solver91311(16872)

Question 434561: 1) Find the fraction form of 8.25 recurring Please help
I keep getting 817/99 but upon checking its not quite right
2) Find the first four terms of the expansion(x-3)^6, this has me stumped Please help, thank you in advance
Click here to see answer by stanbon(57285)

Question 435103: Circumscribed and Inscribed rectangles.
Can someone please show me how to do these?
1: Use circumscribed rectangles to approximate the area under the graph for the function: f(x)=5-(1/4)x^2, for 0<=x<=3.
2: Use inscribed rectangles to approximate the area under the graph for the function f(x)=sqrt(3+x), for -3<=x<=0.
Thank you
Click here to see answer by stanbon(57285)

Question 435298: what is the first term in the sequence for which d=1/3 a7=10 2/3
Click here to see answer by ewatrrr(10682)

Question 435617: The sum of the first n terms of an arithmetic squence is given by the formula; Sn= n/2 (3n-13)=
i) Find the sum of the first two terms
ii) Find the sum of the first three terms
iii) Find the first three terms of the sequence
iv) How many terms of this sequence are required to give a sum of 85?
Click here to see answer by edjones(7569)

Question 435830: find the hundreth term 7,12,17 what is the 100th term?!?!
Click here to see answer by ewatrrr(10682)

Question 436353: Determine whether each sequence could be arithmetic. If so, find the common difference and the next term.
Question 1;
46, 39, 32, 25, 18, ...
Click here to see answer by rwm(914)

Question 436653: this problem is out of my algebra book on Geometric sequences. It is asking for the 1st (which i think is given in the formula) 4th and 8th terms. If you only do one, please do the 8th term
A(n)= -1.1x(-4)^n-1 (i am using x to mean multiply)
Isn't the given -1.1 the first term? I see that the ratio (also given) is a -4. This is giving me the most problems. I get the 4th term as 70.4 and the 8th term as 18022.4 BUT that leaves all the terms alternating in a postive, negative fashion. Didnt think you could do that. Help please.
Thank you
Click here to see answer by stanbon(57285)

Question 436711: 1. find the 7th term in 16, 8, 4,....

2. Find the sum of the first 11 terms in the sequence 4,6,9...

3. What is the sum of the first 100 even numbers
Click here to see answer by stanbon(57285)

Question 436878: Jenny sits and writes:mathsmaths...if she continues in this patter what will the 2007 letter be?
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Question 437863: what is the explicit formula to the sequence 360,180,90,45
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Question 438145: find the nth term of the sequence 5,-10,15,-20
Click here to see answer by robertb(4012)

Question 438147: express the sum using summation notation: 6^2+12^3+18^4+...+48^9
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Question 438181: the following sum is a partial sum in a geometric sequence, use this fact to evaluate the sum.
3+12+...+786432
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Question 438197: hi, i really need help with this. find the sum of the sequence: sigma (2k+7) k=1 and there are 16 terms (on the top of sigma)
Click here to see answer by robertb(4012)

Question 438234: can you please show me how to solve the following problem: show that the statement is true for n^2-n+2 is divisible by 2
Click here to see answer by robertb(4012)

Question 438222: hi there.
i need help with this problem: prove the sum of the first n term of a geometric sequence ...
Click here to see answer by robertb(4012)

Question 438196: Let , for x in [0,1]. Show whether or not
i) converges for each x in [0,1].
ii) converges uniformly on [0,1].
Click here to see answer by robertb(4012)

Question 438225: use the principal mathematical induction to show that the statement is true for all natural numbers n.
9+18+27+...+9n= 9n(n+1)/2
Click here to see answer by Gogonati(809)

Question 438685: Hi, I'm having a really tough time with these two questions. Any help is greatly appreciated, thank you!
1. For the sequence 15,12,9,... find the common difference and the nth term.
2. If 3x-1, 2x+2 and 2x-1 are in Arithmetic Progression, find value of x.

Click here to see answer by richard1234(5390)

Question 438696: Summation: i=1 to 1000 (i^(1/3))
Is this approximately equal to the integral: 1 to 1000 (x^(1/3))dx?
Click here to see answer by richard1234(5390)

Question 438686: Hello, how do I find the first term of the sequence -7,-5,-3,... which is greater than 400. I think it might be 401 but could someone check my answer? Thank you!
Click here to see answer by richard1234(5390)

Question 438761: what is the pattern in: 1,8,27,64??
Click here to see answer by robertb(4012)

Question 439116: Find the sum of n terms of the series
1+2+4+7+11+16++22+...+(nth term)
Click here to see answer by Edwin McCravy(8893)

Question 439410: The product of three consecutive terms in a geometric sequence is -1000, and their sum is 15. Find the common ratio.
Click here to see answer by robertb(4012)

Question 439530: I am having trouble with this question:
Write a formula for the general term (the nth term) of the arithmetic sequence whose second term, a base7 is 4 and whose ninth term, a base is 12.
I am thinking the formula to use is an= a1+(n-1)d
an=1(12-1)4
Is this right?
If you could help me I would appreciate it

Click here to see answer by stanbon(57285)

Question 439699: write varible expression please
Buffy deposits $700 in a college fund with a balance of B. How much money does Buffy have in her account?
Click here to see answer by asuar010(324)

Question 439781: one term of (5m+7n)^8 contains m^5. what is the exponent of n in that term? what is the coefficient of the term?
Click here to see answer by stanbon(57285)

Question 439793: Find the next 2 numbers in this sequence: 3, 3, 5, 6, 8, 12, 12, 24, 17
Click here to see answer by jorel1380(2518)

Question 439933: Hello, how many terms of the sequence -19,-15,-11,... must be taken to give a sum of 98? Thanks :)
Click here to see answer by stanbon(57285)

Question 440227: What number is described by the facts below?
Fact: The number is an integer.
Fact: The cube of the number is less than 50,000.
Fact: The square of the number is greater than 1,250.

Click here to see answer by rwm(914)

Question 440298: what is the rule to find the next term in the sequence 3 7 15 31 63
Click here to see answer by jorel1380(2518)

Question 440909: what is the rule for the sequence 0,3,6,9,12

Click here to see answer by rwm(914)

Question 441352: The 100th term of an arthmetic sequenceis 138, and the common difference is 2. What is the first 3

Click here to see answer by ewatrrr(10682)

Question 441537: If 3x-y=12, then y/3 =

Click here to see answer by unlockmath(1599)

Question 441559: we are not understanding algabra how can u make this easy for us the question reads the sum of marks age and his mothers age is 30 marks mother is 4 times as old as mark how old are mark and his mother if you can show us how this works it would be greatly appreciated
Click here to see answer by rwm(914)

Question 441785: Instructions: For the sequence, describe the pattern, write the next term, & write the rule for the nth term
problem: 4.2, 2.6, 1, (-0.6),(-2.2)...
Click here to see answer by rwm(914)

Question 442493: The 20th term of an arithmetic sequence is 44 and the common difference is 4. Find the nth term
Click here to see answer by stanbon(57285)

Question 442492: The first term of a sequence are 1, -5/2, 2, and -3/2. determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic or geometric, find the fifth term
Click here to see answer by stanbon(57285)

Question 442521: write the sum 1^3 + 2^3 + 3^3 + ... + 100^3 using sigma notation.
Click here to see answer by richard1234(5390)

Question 442536: the second term of a geometric sequence is 10 and the fifth term is 7290. find the nth term
Click here to see answer by stanbon(57285)

Question 442523: write the sum 1/1*2 + 1/2*3 + 1/3*4 + ... + 1/9999*10,000 using sigma notation
Click here to see answer by swincher4391(726)

Question 442537: determine the common ratio, the nth term, and the fifth term for the geometric sequence 8, 16/3, 32/9, 64/27,...,
Click here to see answer by robertb(4012)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645