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

Step-by-step 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:

$\Rightarrow \frac{a+4d}{a+10d}=\frac{5}{2}\\\\\Rightarrow 2a+8d=5a+50d\\\\\Rightarrow 3a+42d=0\\\\\Rightarrow 3(a+14d)=0\\\\\Rightarrow a+14d=0$

Hence, the value of 15th term is 0