Question

plse answer this question step by step​

Answer 1

Answer:

the terms in A.P. are 3, 7, 11, 15 . . . and 199.

Step-by-step explanation:

Consider a and d as the first term and the common difference of an A.P. respectively.  

n th term of an A.P., a_n = a + ( n – 1)d

Sum of n terms of an A.P., S n = n/ 2 [2a + (n – 1)d]

Given that the sum of the first 10 terms is 210.

⇒ 10 / 2 [2a + 9d ] = 210

⇒ 5[ 2a + 9 d ] = 210

⇒2a + 9d = 42 ----------- (1)

15 th term from the last = ( 50 – 15 + 1 ) th = 36 th term from the beginning

⇒ a_36 = a + 35d

Sum of the last 15 terms = 15/2 [2a_36 + ( 15 – 1)d ] = 2565

⇒ 15 / 2 [ 2(a + 35d) + 14d ] = 2565

⇒ 15 [ a + 35d + 7d ] = 2565

⇒a + 42d = 171

eq (2)*2, we get

=> 2a + 84d=342----------(2)  

Now substacting (2) from (1),We get,

75d=300

=> d = 4

Now sub. this in (2) we get a =3

So , From (1) and (2), we have d = 4 and a = 3

Therefore, the terms in A.P. are 3, 7, 11, 15 . . . and 199.

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