If the difference between two consecutive interior angles of a polygon is 5° and smallest angle is 120° then how many sides does the polygon have?
The smallest interior angle is 120 deg. and the corresponding exterior angle is 60 deg. The sum of the exterior angles of the polygon is 360, and the exterior angles are in an AP.Sn = (n/2)[2a +(n-1)d]360 = (n/2)[(2x60) +(n-1)x(-5)], or720 = n[120 -5n + 5], or720 = n[-5n + 125], or144 = n[-n +25], orn^2 - 25n + 144 = 0, or(n-9)(n-16) = 0or n = 9. The figure is an irregular nonagon. The sum of the nine exterior angles which are 60,55,50,45,40,35,30,25,20 = 360.Check: Sn = (9/2)[2*20 + (9–1)*5] = (9/2)[40 +8*5]] = (9/2)[40+40] = 9*80/2 = 360. Correct.n = 9. The figure is an irregular nonagon.
In the increasing sequence below, the first term is y and the difference between any two consecutive terms is?
In the increasing sequence below, the first term is y and the difference between any two consecutive terms is 3. What is the value of the fourth term in the sequence? y, 2y + 7, y + 6, … (A) – 4 (B) 2 (C) 5 (D) 13 (E) 19
21. In the increasing sequence below, the first term is y and the difference between any two consecutive term?
The 4th term = 5 Answer (C) If the difference in consecutive terms = 3 it means that (2y + 7) - y = 3 (ie the second term minus the first term) Remove the bracket and simplify y + 7 = 3 y = - 4 Therefore the terms are y = -4 2y + 7 = -8 + 7 = -1 y + 6 = - 4 + 6 = 2 Sequence is -4, -1, 2.........and then 5,8,11 etc etc
How do I find the sum of a sequence whose common difference is in a.p.?
I will provide you a shortcut which i learned in my class 10th :P.the general term of a series whose common difference is in AP is ax^2 + bx + cwhere a, b and c are constants.NOW, for first term put x=1 and we know that first term of the series is 1so, a + b + c = 1…….(i)for second term put x=2 and we know that second term is 3so, 4a + 2b + c = 3…..(ii)for third term put x=3 and we know that third term is 6so, 9a + 3b + c = 6…….(iii)solving these three equations will give you a= 1/2 b=1/2 and c = 0so the general term for the series is x^2/2 + x/2.now take the sum(∑(n^2) + ∑(n))/2S(n)=(1/2)*(((n*n+1)/2)+(n*(n+1)*(2n+1)/6))Put n= 13 (as per the example) and we will get the sum as 455 :)
What is the difference between Fibonacci sequence and arithmetic progression?
In arithmetic progression , the difference between consecutive terms is constant. Arithmetic progression - WikipediaIn Fibonacci sequence, the difference between consecutive terms is not constant. In fact, it keeps on increasing .Fibonacci number - Wikipedia
Consecutive integers?
Someone explain the difference between these two and how to set them up and solve. Find the second of two consecutive integers if the second is 13 less than twice the first. And Find the smaller of two consecutive odd integers if the larger is 20 less than three times the smaller.
How do I directly write the nth term of a series whose difference of difference is in arithmetic progression?
I know the nth term of a sequence the difference of whose 2 consecutive terms forms an Arithmetic progression. The question is how to find the nth term of a series whose difference of difference forms an AP(which i can't answer). However, my answer here is the nth term of the series whose differences(not difference of difference) form an AP.We are dealing with 2 kinds of series here-The original series which is not in APThe second series(AP series) formed by the difference of consecutive terms of the original series. Now, THIS is in AP.Now, to find the nth term of the original series, we need 3 known values-The 1st term of the original seriesThe 1st term of the AP seriesThe common difference of the AP series.The formula for the nth term of the series is-Tn= a + (n-1)[2m +(n-2)d]/2where Tn= nth term of the seriesa= First term of the seriesm= first term of the AP seriesd= common difference of the AP seriesI have shown the working in the picture. My cam quality is not good. Hope the working is clear. This is what i derived. If there is a better formula for the nth term, please share it with us. Any suggestions and queries are welcome. :) (y)
If a, b, c, d and e are five consecutive odd numbers then their average is?
Answer for your question is 4. None of theseSince they are consecutive odd numbers all the terms are in AP with a common difference 2.So the first term is a.Second term, b= a+2Third term, c = b+2 = a+2+2 = a+4Fourth term, d = c+2 = a+4+2 = a+6Fifth term, e = d+2 = a+6+2 = a+8So average=( a+b+c+d+e)/5Average = (a+(a+2)+(a+4)+(a+6)+(a+8))/5Average = (5a+20)/5Average = a+4Therefore the answer is 4. None of these
The average of 3 consecutive even numbers is A. If the next 5 consecutive numbers are added, then what’s the average of these 8 numbers?
The numbers areA-2, A, A +2Fir odd number of terms with same difference between two consecutive terms, the average us always the middle number. When there are 3 numbers, average will be middle numberAfter adding 5 more terms, total terms = 3+5 = 8 termsWhen number of terms are evenAverage = (1st term + last term)/2 or= (Middle two terms) / 2The numbers areA-2, A, A+2, A+4, A+6, A+8, A+10, A+121st and last terms are A-2, A+12Average = (A-2 +A+12)/2= (A+10)/2 (Ans)= A/2 + 5 (Ans)
If you have a sequence of 3, 6, 9, 12, what is the nth term and how do you work it out?
From viewing the sequence it is an Arithmetic Progression where the first term (a) is 3 and the Common Difference (d) is 3.The equation for the nth term is a + (n-1)d.We can find the fourth term as 3 +(4–1)*3 = 3 + 9 = 12. Proved.The 21 first term will thus be 3 +(21–1)*3 = 3 + 20*3 = 63.