Question

what is the common difference of a 43-term arithmetic sequence where the first term is -13 and the sum is 9374

Answer 1

first find the last term using
\[n(first term+last term)/2=summation\]

Answer 2

There is no given last term, How would I find it?

Answer 3

that is what u have to find
n=43
first term=-13
summation=9374
now put them in the formula and find the last term

Answer 4

43(-13+lastterm)/2=9374

Answer 5

yeah :)

Answer 6

So then would I multiply -13 and (x) by 43 to give me
(-559+ 43(x) )/2= 9347

Answer 7

\[\frac{ 43(-13+last term) }{ 2 }=9374\]
\[-13+lasterm=\frac{ 9374*2 }{43 }\]
\[last term=436+13=449\]
ok now use this formula
\[last term=first term+(n-1)*(common ratio)\]
your last term=449
first term=-13
n=43 so
\[449=-13+(43-1)*common ratio=-13+42*(common ratio)\]
common ratio=11
do u get it??

Answer 8

Yes, Thankyou.

Answer 9

np:)