Question

the 37th term of an ap is 60 and the 60th term of the ap is 84. then the 14th term of the ap.​

Answer 1

Answer:

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Answer 2

Given : 37th term of an ap is 60 and the 60th term of the ap is 84  

To Find : the 14th term of the ap.​

Solution:

37th term of an ap is 60  

60th term of the ap is 84

aₙ = a + (n-1)d

a = first term

n = number of term

d = common difference

a₃₇ = a + 36d  =  60

a₆₀ = a + 59d  = 84

=>  23d  = 24

=> d = 24/23

a + 36d  =  60

=> a  + 36(24/23)  = 60

=> a =  516/23

14th term of the ap.​

a₁₄ = a  + 13d

516/23 + 13(24/23)

=  828/23

=  36

14th term of the ap.  = 36

or simpler way without difficult calculations

23d  = 24

a + 13d  =  a + 36d   - 23d

= 60 - 24

= 36

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