Question

Find the sum of the first 19 terms of the AP whose n th term is given by tn=7-4n?

Answer 1

An=7-4n
Therefore
A1=7-4(1)=7-4=3
A2=7-4(2)=7-8=-1

Now d=An - A(n-1)
So... d =A2-A1
Thus....d=-1-3=-4
Hence d=-4




Here a=3,d=-4



Now Sn=(n/2)[2a+(n-1)d]
Thus
S19= (19/2)[2(3)+18(-4)]
S19={19×(6-72)}/2
S19={19×(-66)}/2
S19={19 ×(-33)}
S19=-627




Hence sum of 19 terms of the a.p. Is -627




Hope it helps