Question

the 10th term and the 18 term of an A.P are 25 and 41 respectively find the 1term and the common difference and the 34th term and n such that tn=87​

Answer 1

Answer:

First term = 7

Common Difference = 2

34th term = 73

n = 41 if tn=87

Step-by-step explanation:

We are given that 10th term and the 18 term of an A.P are 25 and 41 respectively i.e.,

              $a_1_0$ = 25                                              $a_1_8$ = 41

     ⇒ a + (10 - 1 )*d = 25                             ⇒ a + (18 - 1 )*d = 41

Here, a = first term and d = common difference.

     ⇒ a + 9*d = 25                                       ⇒ a + 17*d = 41

     ⇒  a = 25 - 9*d -------- [Equation 1]        ⇒  a = 41 - 17*d ------- [Equation 2]

Equating equation 1 and 2 we get,

         ⇒  25 - 9*d = 41 - 17*d

         ⇒   17*d - 9*d = 41 - 25      ⇒ 8*d = 16

Therefore, common difference,d = 2     and    First term,a = 25 - 9*2 = 7

34th term,$a_3_4$ = a + (34 - 1 )*d = 7 + 33*2 = 73 .

Also, we are given $t_n$ = 87 and we have to find n ;

            ⇒  a + (n-1)*d = 87  

            ⇒  7 + (n-1)*2 = 87

            ⇒ (n-1)*2 = 80    ⇒  n - 1 = 40

Therefore, n = 41 if $t_n$ = 87 .