Question

In an AP the first term is –5 and the last term is 45. If sum of all numbers in AP is 120 then how many terms are there ? What is the common difference ? (3)

Answer 1

Answer:-

a=-5

an=45

Sn=120

Sn=n/2(a+an)

120=n/2(-5+45)

120=n/2(40)

120=20n

n=120/20

n=6

Therefore , number of terms =6

an=a+(n-1)d

45=(-5)+(6-1)d

45+5=5d

50=5d

d=50/5

d=10

Therefore , common difference = 10

Answer 2

Answer:

solution is given below

Step-by-step explanation:

a = -5

L= 45

n = ?

Sn = 120

From the gauss formula

Sn = n/2 [a + L]

120 = n/2 [ -5 + 45]

120 x 2 = n [ 40 ]

240 = 40n

240/40 = n = 6

and the common difference is

An = a + (n-1) x d

45 = -5 + (6-1)d

50= 5d

50/5

= d =10

hope you help this solution