Question

In an A. P., the first term is - 5 and last term is 45. If sum of all numbers in the A. P. is 120, then how many terms are there? What is the common difference?

Answer 1

Sn=n/2(a+an)
120=n/2( -5+45)
240=n(40)
n=240/40
n=6

Answer 2

Let d be the c.d and n be the total no of terms
a=-5
Last term=45
a+(n-1)d=45
(n-1)d=50---------------------------eq(1)+
Sn=120
n/2(2a+(n-1)d)=120
n(-10+(n-1)d)=240
From eq(1)
n{-10+(n-1)50/(n-1)}=240
n(-10+50)=240
n=240/40
n=6
d=10