Answer:
The first term is -5 and the common difference is 4
tn = -9+4n
Explanation:
Sn = 2n^2 -7n
The formula for the arithmetic sum is given by
Sn =n/2 (2a1 + d(n-1))
We set these equal
2n^2 -7n = n/2 (2a1 + d(n-1))
Factor out an n on the left side
n(2n-7) = n/2 (2a1 + d(n-1))
Divide each side by n
n/n(2n-7) = n/2*1/n (2a1 + d(n-1))
(2n-7) = 1/2 (2a1 + d(n-1))
Multiply by 2
2(2n-7) = 2*1/2 (2a1 + d(n-1))
2(2n-7) = (2a1 + d(n-1))
Distribute
4n -14 = 2a1 +dn -d
The n terms have to be equal
4n = dn
d=4
The constant terms have to be equal
-14 = 2a1 -d
we know d
-14 = 2a1 -4
Add 4 to each side
-14+4 = 2a1-4+4
-10 = 2a1
Divide by 2
-10/2 =2a1/2
-5 =a1
The first term is -5 and the common difference is 4
The term ( you call it tn I call it an)
an = a1+d(n-1)
an = -5+4(n-1)
an = -5 +4n-4
an = -9+4n