The Student Room Group
Reply 1
neomilan
Last question on this awful topic !

Find the sum of all the integers between 1 and 1000 divisible by 7.
Hence or otherwise, evalute
Unparseable latex formula:

[br]\[[br]\sum_{r=1}^{142} (7r+2)[br]\][br]



For the first bit i did:
Sn=1422(2×7+(1421)7)[br]S_n = \frac{142}{2} (2\times7 + (142-1)7)[br]
i got 71071
is that correct?

but then i got a different asnwer for the sigma part


The first term is 1*7 + 2 = 9. 2nd Term: 14 + 2= 16, 3rd Term= 23
Reply 2
Therefore '2a' is 18, not 14.
Reply 3
v1oXx-
Therefore '2a' is 18, not 14.


but the first part says: "Find the sum of all the integers between 1 and 1000 divisible by 7."
the way i would try it was to do:
sigma [142,r] = 7r
for the first part ["Find the sum of all the integers between 1 and 1000 divisible by 7"]
which you got right [first post]

then then leads onto the second part of the question
Reply 5
gobbledygook88
the way i would try it was to do:
sigma [142,r] = 7r
for the first part ["Find the sum of all the integers between 1 and 1000 divisible by 7"]
which you got right [first post]

then then leads onto the second part of the question


that's exactly what i did, but then i was wondering why the first part of the question has a different answer to the second part of the question with the sigma
its cause in the second part of the question has requires you to add in an extra 2 for each term:
the question:
sigma [142,] 7r +2

which then equals:
(7 x sigma[142,r] r) + (2 x 142) = 71355
as you can see, the first part relates to the second part of the question
in the 1st question it is just multiples of 7, in the second part it is asking for (((((7r+2)))))