Question

1. the ratio of first to the last of n A.m.'s between 5 and 35 is 1:4. The value of n is
a 9
b. 11
10
d. 19​

Answer 1

Given : The ratio of first to the last of n A.M's between 5 and 35 is 1:4.

To Find : The value of n

Solution:

First number = 5

Last number = 35

Inserted n A.M's

Hence total numbers =  n + 2

a = 5

n + 2 th Term = 35

n + 2 th term  = a + (n  +2 - 1)d

=> 35 = 5 + (n + 1)d

=> 30 = (n + 1)d

First AM = 5 + d

Last AM = 35 - d

The ratio of first to the last  is  1: 4

=> (5 + d)/(35 - d) = 1/4

=> 20 + 4d = 35 - d

=> 5d = 15

=> d = 3

30 = (n + 1)d

=> 30 = (n + 1)3

=> 10 = n + 1

=> n = 9

The value of n is 9

Correct option is a)

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Answer 2

Answer:

Option A is the correct answer.