Answer: The value of 15th term is 0
Step-by-step explanation:
The nth-terms of an AP is written as [tex]a+(n-1)d[/tex]
where,
a = first term
n = number of term
d = common difference
5th tem will be = [tex]a+4d[/tex]
11th tem will be = [tex]a+10d[/tex]
15th tem will be = [tex]a+14d[/tex]
The given ratio between 5th and 11th term is 5 : 2
Taking the ratios:
[tex]\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[/tex]
Hence, the value of 15th term is 0
