Question

4. If the ratio of 5 th term to 11th term of an A.P. is 5:2, then the value of

term is
15th

Answer 1

Answer: The value of 15th term is 0

Explanation:

The nth-terms of an AP is written as
`a+(n-1)d`

where,

a = first term

n = number of term

d = common difference

5th tem will be =
`a+4d`

11th tem will be =
`a+10d`

15th tem will be =
`a+14d`

The given ratio between 5th and 11th term is 5 : 2

Taking the ratios:

`\Rightarrow (a+4d)/(a+10d)=(5)/(2)\\\\\Rightarrow 2a+8d=5a+50d\\\\\Rightarrow 3a+42d=0\\\\\Rightarrow 3(a+14d)=0\\\\\Rightarrow a+14d=0`

Hence, the value of 15th term is 0