Which term of the A.P. 3, 15, 27, 39,..... will be 120 more than its

1.	Which term of the A.P. 3, 15, 27, 39,..... will be 120 more than its 21st term?
Answer» a = 3, d = 15 – 3 = 12 Let last term be a_n a_n = a + (n – 1) d = 3 + (n – 1) 12 = 12n – 9 (i) a₂₁ = a + 20d = 3 + 20(12) = 243 Now, the term is 120 more than the 21^st term a_n = 120 + a₂₁ = 120 + 243 = 363 Putting this value in (i), we get 363 = 12n – 9 12n = 363 + 9 n = 31 Hence, 31^st term of given A.P. is 120 more than its 21^st term

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

Answer»

a = 3, d = 15 – 3 = 12

Let last term be a_n

a_n = a + (n – 1) d

= 3 + (n – 1) 12

= 12n – 9 (i)

a₂₁ = a + 20d

= 3 + 20(12) = 243

Now, the term is 120 more than the 21^st term

a_n = 120 + a₂₁

= 120 + 243

= 363

Putting this value in (i), we get

363 = 12n – 9

12n = 363 + 9

n = 31

Hence, 31^st term of given A.P. is 120 more than its 21^st term