Respuesta :

[tex]\bf \textit{the }n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_1=\textit{first term in the sequence}\\ d=\textit{common difference} \end{cases} \\\\\\ a_{25}=a_1+(25-1)d\impliedby 25^{th}\ term[/tex]

plug in the provided values then

Answer:  The required 25-th term of the given sequence is 125.  

Step-by-step explanation: We are given to find the 25-th term of a sequence with first term and common difference as follows :

a = 5   and   d = 5.      

Since we are dealing with common difference, so the given sequence must be an arithmetic one.

We know that

the n-th term of an arithmetic sequence with first term a and common difference d is given by

[tex]a_n=a+(n-1)d.[/tex]      

Therefore, the 25-th term of the given arithmetic sequence will be

[tex]a_{25}=a+(25-1)d=5+24\times5=5+120=125.[/tex]

Thus, the required 25-th term of the given sequence is 125.          

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