Question

If 5th term of an ap is 1/9 and 9th term is 1/5. Find the common difference,first term and sum of 45th term​

Answer 1

Step-by-step explanation:

a5 = 1/9

or, a + 4d = 1/9

or, a = 1/9 - 4d _____(i)

a9 = 1/5

or, a + 8d = 1/5

or, a = 1/5 - 8d _____(ii)

Equating equations (i) and (ii), we get,

1/9 - 4d = 1/5 - 8d

-4d + 8d = 1/5 - 1/9

4d = (9-5)/45

4d = 4/45

d = 1/45

∴ Common Difference = 1/45

Then, Putting the value of d in eqn (i),

a = 1/9 - 4/45

= (5-4)/45

= 1/45

∴ a45 = a + 44d

= 1/45 + 44/45

= (1 + 44)/45

= 45/45

= 1

∴ 45th term of this AP = 1