Question

Q.1  The 5th and the 8th terms of an arithmetic sequence are in the ratio 1: 7.

(a) What is the ratio between the 6th  and 15th terms?
(b) The 7th term of this sequence is 10. What is the 22th term?

Answer 1

nth term of an AP = a + (n-1)d
Ratio of 5th and 8th terms = 1 : 7
a+4d : a+7d = 1 : 7

7(a+4d) = a + 7d
7a + 28d -a - 7d = 0
6a + 21 d = 0
2a = -7d

$a = \frac{-7d}{2} = -3.5d$

i) Ratio between 6th and 15th terms = a+5d : a + 14d

= -3.5d + 5d : -3.5d + 14d

=  1.5d : 10.5 d
=  1 : 7

ii) 7th term of the sequence = 10
  a + 6d = 10

-3.5d + 6d = 10

2.5 d = 10

d = 4
a = (-3.5)*4 = -14

22nd term = a + 21d

= -14 + 21(4)

= -14 + 84

=  70