Question

In an arithmetic​ sequence, the nth term an is given by the formula An=a1+(n−1)d​, where a1

Answer 1

Answer:

88

Step-by-step explanation:

We are given that in arithmetic sequence , the nth term $a_n$ is given by the formula

$A_n=a_1+(n-1)d$

Where $a_1=first term$

d=Common difference

In an geometric sequence, the nth term is given by

$a_n=a_1r^{n-1}$

Where r= Common ratio

1,4,7,10,..

We have to find 30th term.

$a_1=1,a_2=4,a_3=7,a_4=10$

$d=a_2-a_1=4-1=3$

$d=a_3-a_2=7-4=3$

$d=a_4-a_3=10-7=3$

$r_1=\frac{a_2}{a_1}=\frac{4}{1}=4$

$r_2=\frac{a_3}{a_2}=\frac{7}{4}$

$r_1\neq r_2$

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

$a_{30}=1+(30-1)(3)=1+29(3)=1+87=88$

Hence, the 30th term of sequence is 88.