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?

Given, first term a = – 5

Last term t_n = 45

Sum of n terms S_n = 120

To find no of terms “n”

Using Sum of n terms of an A.P. formula

where n = no. of terms

S_n = sum of n terms

Now, on substituting given value in formula we get,

⇒ 120 = 20 n

To find the common difference ‘d’

We use n^th term of an A.P. formula

t_n = a + (n – 1)d

where n = no. of terms

a = first term

d = common difference

t_n = n^th terms

Thus, on substituting all values we get,

⇒ t₆ = – 5 + (6 – 1)d

⇒ 45 = – 5 + 5d

⇒ 5d = 45 + 5 = 50

Thus, common difference is 10