Question

Write the sum using summation notation, assuming the suggested pattern continues.

-10 - 2 + 6 + 14 + ... + 110

Answer 1

as -2 -(-10) =8
6- (-2) =8
thus the above pattern is in AP

Answer 2

AP means Arithmetic sequence hence
here the first term is -10 and the common difference is +8
first we have to find the number of terms involved say n

Answer 3

how would I find that?

Answer 4

here an the nth tern is 110
so we have
110 = -10 + (n-1)*8
thus n-1 =(110+10)/8
or n-1 =15
hence n =16
that is to saty 110 is the 16th term of the given pattern

Answer 5

so far I have \[\sum_{n}^{n=0} -10 + 8 (n)\]

Answer 6

so the summation all the numbers in the given pattern is yup correct the limits are now from 0 to 15 (instead of 16 as the start point is 0) as we know the value of n

Answer 7

i hope you can do futher
this may result as
-10*16 + 8*(1+2+3+4...........15)
=-160 + 8*15*16/2 and so on ...

Answer 8

\[\sum_{n=0}^{15} -10 + 8n

or \sum_{n=0}^{15} -80n\]

Answer 9

first one..

Answer 10

okay so you don't add them together, just leave them as they are?

Answer 11

as they are not alike terms..

Answer 12

now the sum equals
-10*16 + 8*(1+2+3+4...........15)
=-160 + 8*15*16/2 and so on ...

Answer 13

i hope that you will be able to carry on further...

Answer 14

I understand now. Sorry for being difficult I forget the simple things sometimes :/ oops

Answer 15

this is an AP in which first term is -10 and last term is 110
having common difference = -2-(-10)=8
first u have to find total no of terms
any term=a+(n-1)d
n=no of term
a=first term
d=common difference
110=-10+(n-1)8
n=16
sum of all terms=
n/2 * (2a+(n-1)d)
16/2 * (-20+(15)(8))
8*100
=800

Answer 16

@yesy7
its ok

Answer 17

Thank you @nirmalnema for explaining as well :)

Answer 18

its ok..!!

Answer 19

@yesy7
what nirmelnema has done is also an alternate way of finding the required sum
further since you know the last term we can alternatively (rather more easy) use

sum =n/2 *(first term +last term)
hence sum =16/2 (-10 +110) = 8* 100 =800

Answer 20

Okay, cool!