Which term of the A.P. 3, 10, 17, …. will be 84 more than its 13th

1.	Which term of the A.P. 3, 10, 17, …. will be 84 more than its 13th term ?
Answer» Given, A.P. 3, 10, 17, …. Here, a = 3 and d = 10 – 3 = 7 According the question, a_n = a₁₃ + 84 Using a_n = a + (n – 1)d, 3 + (n – 1)7 = 3 + (13 – 1)7 + 84 3 + 7n – 7 = 3 + 84 + 84 7n = 168 + 7 n = 175/7 n = 25 Therefore, it the 25^th term which is 84 more than its 13^th term.

Which term of the A.P. 3, 10, 17, …. will be 84 more than its 13th term ?

Answer»

Given, A.P. 3, 10, 17, ….

Here, a = 3 and d = 10 – 3 = 7

According the question,

a_n = a₁₃ + 84

Using a_n = a + (n – 1)d,

3 + (n – 1)7 = 3 + (13 – 1)7 + 84

3 + 7n – 7 = 3 + 84 + 84

7n = 168 + 7

n = 175/7

n = 25

Therefore, it the 25^th term which is 84 more than its 13^th term.