Which term of the A.P 3, 10, 17, ………. Will be 84 more than its 1

1.	Which term of the A.P 3, 10, 17, ………. Will be 84 more than its 13th term?
Answer» As 3, 10, 17... constitute terms of an A.P a= 3 n = 13 d = 7 a_n = a + (n-1)d = 3 + 12 x 7 = 87 According to the question, a_n = 87 + 84 = 171 3 + (n-1)7 = 171 (n-1)7 = 168 n-1 = 168/7 n = 24 +1 =25 25th term will be 84 more than 13th term Let the nth term be 84 more than the 13th term. Now a/q, a=3, d = 10 - 3 = 7 So, 13th term= a + 12 d = 3 + 12 x 7 = 87 Then nth term = 84 + 87 = 171 171 = a + (n -1) d 171 = 3 + (n-1) x 7 (171 -3)/7+1 = n 168/7+1 = n 24+1 = 25 = n Therefore 25th term of the ap will be 84 more than 13th term.

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

Answer»

As 3, 10, 17... constitute terms of an A.P
a= 3
n = 13
d = 7
a_n = a + (n-1)d = 3 + 12 x 7 = 87
According to the question,
a_n = 87 + 84 = 171
3 + (n-1)7 = 171
(n-1)7 = 168
n-1 = 168/7
n = 24 +1 =25

25th term will be 84 more than 13th term

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

Now a/q,

a=3, d = 10 - 3 = 7

So, 13th term= a + 12 d = 3 + 12 x 7 = 87

Then nth term = 84 + 87 = 171

171 = a + (n -1) d

171 = 3 + (n-1) x 7

(171 -3)/7+1 = n

168/7+1 = n

24+1 = 25 = n

Therefore 25th term of the ap will be 84 more than 13th term.

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