Answer:
88
Step-by-step explanation:
We are given that in arithmetic sequence , the nth term [tex]a_n[/tex] is given by the formula
[tex]A_n=a_1+(n-1)d[/tex]
Where [tex]a_1=first term[/tex]
d=Common difference
In an geometric sequence, the nth term is given by
[tex]a_n=a_1r^{n-1}[/tex]
Where r= Common ratio
1,4,7,10,..
We have to find 30th term.
[tex]a_1=1,a_2=4,a_3=7,a_4=10[/tex]
[tex]d=a_2-a_1=4-1=3[/tex]
[tex]d=a_3-a_2=7-4=3[/tex]
[tex]d=a_4-a_3=10-7=3[/tex]
[tex]r_1=\frac{a_2}{a_1}=\frac{4}{1}=4[/tex]
[tex]r_2=\frac{a_3}{a_2}=\frac{7}{4}[/tex]
[tex]r_1\neq r_2[/tex]
Therefore, given sequence is an arithmetic sequence because the difference between consecutive terms is constant.
Substitute n=30 , d=3 a=1 in the given formula of arithmetic sequence
Then, we get
[tex]a_{30}=1+(30-1)(3)=1+29(3)=1+87=88[/tex]
Hence, the 30th term of sequence is 88.
