Which term of the A.P 3,15,27,39...will be 120 more than it’s 21st term ?

31 st term

Step-by-step explanation:

The n th term of an AP is calculated as

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = 15 - 3 = 12

Calculate the 21 st term

a₂₁ = 3 + (20 × 12 ) = 3 + 240 = 243

Add 120 to 243 = 363, thus

3 + 12(n - 1) = 363 ( subtract 3 from both sides )

12(n - 1) = 360 ( divide both sides by 12 )

n - 1 = 30 ( add 1 to both sides )

n = 31

That is the 31 st term is 120 more than the 21 st term