Question

which term of the AP 3 , 10 , 17, ......... will be 84 more than its 13th term

Answer 1

Given AP is 3,10,17.....

First-term a = 3.

Common difference d = 10 - 3 = 7.

We know that Sum of n terms an = a + (n - 1) * d       ------ (1)

                                                     a13  = 3 + (13 - 1) * 7

                                                             = 3 + 12 * 7

                                                            = 3 + 84

                                                            = 87.


Let the nth term be 84 more than its 13th term.

an = a13 + 84

     = 87 + 84

     = 171.             -----------(2)
 

Substitute (2) in (1), we get

171 = 3 + (n - 1) * 7

171 - 3 = (n - 1) * 7

168 = (n - 1)  * 7

168 = 7n - 7

168 + 7 = 7n

175 = 7n

n = 25.


Therefore the required term is the 25th term.

Hope this helps!

Answer 2

Answer:

25

Step-by-step explanation:

Given AP is 3,10,17.....

First-term a = 3.

Common difference d = 10 - 3 = 7.

We know that Sum of n terms an = a + (n - 1) * d       ------ (1)

                                                     a13  = 3 + (13 - 1) * 7

                                                             = 3 + 12 * 7

                                                            = 3 + 84

                                                            = 87.

Let the nth term be 84 more than its 13th term.

an = a13 + 84

     = 87 + 84

     = 171.             -----------(2)

 

Substitute (2) in (1), we get

171 = 3 + (n - 1) * 7

171 - 3 = (n - 1) * 7

168 = (n - 1)  * 7

168 = 7n - 7

168 + 7 = 7n

175 = 7n

n = 25.

Hope This helps you. ....