seq question

[vardhans83]

john did 1320 questions in 20 days. each day after the first day, he did 4 questions more than the previous day. how many questions did he do on day 6

[Night reader]

a(n)=a(n-1)+4, note please we have sequence of numbers here ;
sum of a(n=1...20)=1,320
a(1), a(1)+4, a(1)+8, ... a(1) + 4*19 <--- this a(20) actually
calculate the sum of all 4s from a(2) to a(20) ---> (4+76)/2 *19 = 40*19 =760;
calculate all a(1)-s ---> 20*a(1)
write down equation and solve for a(1) ---> 20*a(1)+760=1,320, a(1)=28;
now find a(6) ---> a(1) + 4*5 = 28+20 =48

the answer should be a(6) is 48, am I correct?
oppps

john did 1320 questions in 20 days. each day after the first day, he did 4 questions more than the previous day. how many questions did he do on day 6

[vardhans83]

The issue is i just have the questions with no solutions...sorry! i know its annoying.

i do not understand this part. Could you please explain?: calculate the sum of all 4s from a(2) to a(20) ---> (4+76)/2 *19 = 40*19 =760;

[Night reader]

i was asking your attention here - sequence of numbers, i.e. the numbers are consecutive NOT integers like 1,2,3,4 ... BUT numbers like 120, 130, 140 ... OR 2,6,10,14 ... We are using the following method for consecutive numbers (including integers) --> find mean (mean=median) multiply mean by the number of units in the consecutive sequence. Here mean is 40, by finding median (4+76)/2 and we multiply this by 19 to calculate the sum of all units in the consecutive sequence, i.e. 4+8+16+... 76=760

The issue is i just have the questions with no solutions...sorry! i know its annoying.

i do not understand this part. Could you please explain?: calculate the sum of all 4s from a(2) to a(20) ---> (4+76)/2 *19 = 40*19 =760;

john did 1320 questions in 20 days. each day after the first day, he did 4 questions more than the previous day. how many questions did he do on day 6

[GMATGuruNY]

john did 1320 questions in 20 days. each day after the first day, he did 4 questions more than the previous day. how many questions did he do on day 6

The difference between each pair of successive days is 4.
When values are evenly spaced, the median = the average.

Average = 1320/20 = 66.
Thus, the median value -- the average of day 10 and day 11 -- is 66.
Thus, day 10 = 64 and day 11 = 68.
Since the value on each day is 4 more than the value on the previous day:
Day 6 = day 10 - 4 days = 64 - 4*4 = 48.

[Night reader]

Hi Mitch, very interesting method the difference in my approach was find average and a(1) while you found an average and a(10), a(11) in order to find a(6).
Thanks

john did 1320 questions in 20 days. each day after the first day, he did 4 questions more than the previous day. how many questions did he do on day 6

The difference between each pair of successive days is 4.
When values are evenly spaced, the median = the average.

Average = 1320/20 = 66.
Thus, the median value -- the average of day 10 and day 11 -- is 66.
Thus, day 10 = 64 and day 11 = 68.
Since the value on each day is 4 more than the value on the previous day:
Day 6 = day 10 - 4 days = 64 - 4*4 = 48.

[rohu27]

for an equally spaced set = mean=median=(a1+an)/2 whee an=last term of the sequence.
sum of the entire sequence = mean*no. of terms =(a1+an)/2 *n

it applies for all eqaully spaced sets ? am i right?

[Night reader]

yes it does as long as math makes sense

for an equally spaced set = mean=median=(a1+an)/2 whee an=last term of the sequence.
sum of the entire sequence = mean*no. of terms =(a1+an)/2 *n

it applies for all eqaully spaced sets ? am i right?

[Anurag@Gurome]

john did 1320 questions in 20 days. each day after the first day, he did 4 questions more than the previous day. how many questions did he do on day 6

Solution:
Let john do q questions on day 1.
So, he does q+4 = q+4*1 questions on day 2, q+8 = q+4*2 questions on day 3, q+12 = q+4*3 on day 4 and so on.
So, observing the pattern, we can say that he does q + 4*19 questions on day 20.
Also, the sum of all questions is 1320.
So, q + (q+4) + (q+8)....+(q+76) = 1320.
Or , 20q+(4+8+..+76) = 1320.
Let us calculate the sum 4+8+...+76.
Let S = 4+8+12... 72+76-------------(1)
Or S =76+72+........ +4-------------(2), writing backwards.
Adding, (1) and (2) we get 2S = 19*80.
Or S = 19*80/2 = 760.
So 20q+760 = 1320.
Or 20q = 1320 - 760 = 560.
Or q = 28.
Hence, on day 6, he will do q+4*5 = 28+20 = 48 questions.