sequences

[12345678]

‘Find the number of terms in the arithmetic sequence needed to form the given sum’
3+7+11+… Sum=820
a=3
d=4
Sn = 1/2n (2a + (n-1)d)
820 = 1/2n ((2 * 3) + (n – 1) x 4)
820 = 1/2n(6 + (n-1)4)
820 = 1/2n (4n + 2)
820 = 2n^2 + n
I was wondering if somebody could help me find n from the last line please

 

[srmichael]

‘Find the number of terms in the arithmetic sequence needed to form the given sum’
3+7+11+… Sum=820
a=3
d=4
Sn = 1/2n (2a + (n-1)d)
820 = 1/2n ((2 * 3) + (n – 1) x 4)
820 = 1/2n(6 + (n-1)4)
820 = 1/2n (4n + 2)
820 = 2n^2 + n
I was wondering if somebody could help me find n from the last line please

You have \(\displaystyle 2n^2+n=820\)

Now factor and solve \(\displaystyle 2n^2+n-820=0\)

Do you not know how to factor or did you not know you had to factor?

 

[pka]

‘Find the number of terms in the arithmetic sequence needed to form the given sum’
3+7+11+… Sum=820
a=3
d=4
Sn = 1/2n (2a + (n-1)d)
820 = 1/2n ((2 * 3) + (n – 1) x 4)
820 = 1/2n(6 + (n-1)4)
820 = 1/2n (4n + 2)
820 = 2n^2 + n

Have a look at this webpage.

 

[12345678]

Cheers for replys- not sure why I didn't think of trying to factorise it tbh. Saw 820 and just assumed I would have to do something else as this is a new topic;
(2n + 41) (n - 20)
ignore -20.5 as cant have a negative number of sequences; n= 20.