Question

n terms lie between 7 and 49 in an ap if the ratio of the fourth term and the n-1 term is 5:4 then find the value of n​

Answer 1

Correcting the question:

  3rd term : (n - 1)th term = 4 : 5

Solution:

The question states a definite AP as follows,

   7, ... ( n terms ) ..., 49

Thus there exists (n + 2) terms in the AP.

Given, first term, a = 7

and (n + 2)th term = 49

  or, a + {(n + 2) - 1}d = 49

  or, a + (n + 1)d = 49

  or, (n + 1)d = 49 - 7 = 42

  or, d = 42 / (n + 1)

Also given that,

    3rd term : (n - 1)th term = 4 : 5

or, (a + 3d) : {a + (n - 1)d} = 4 : 5

or, (7 + 3d) / {7 + (n - 1)d} = 4 / 5

or, 35 + 15d = 28 + (4n - 4)d

or, (4n - 19)d = 7

or, {(4n - 19) * 42 / (n + 1)} = 7

or, 42 (4n - 19) = 7 (n + 1)

or, 168n - 798 = 7n + 7

or, 161n = 805

or, n = 5

Therefore, the value of n is 5

Note:

    The ratio of 3rd term and (n - 1) th term is given. But whose terms are those?

    They both belong to those n terms which were inserted between 7 and 49. Let A₁, A₂, A₃, ..., Aₙ be those n terms lying between 7 and 49, and d be the common ratio with the first term a.

Then A₁ = a + d

        A₂ = a + 2d

        ...   ...   ...

        Aₙ = a + nd

Answer 2

Answer:

there is some mistake in data

Step-by-step explanation:

N terms lie between 7 and 49 in an ap

=> total Term including 7 & 49 are N + 2  Terms

ratio of the fourth term and the n-1 term is 5:4

=> Fourth Term = a + 3d  =  7 + 3d

&  N- 1 The term   =  49 - 3d

(7 + 3d)/(49 - 3d)  = 5/4

=> 28 + 12d = 245 - 15d

=> 27d = 217

49 = 7 + (N + 1)d

=> 49 = 7 + (N + 1)(217/27)

=> 42 * 27 / 217  = N + 1

=> N = 4.22

=> there is some mistake in data