Question

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

is the first term and d is the common difference.​ Similarly, in a geometric​ sequence, the nth term is given by an=a1•rn−1.

Here r is the common ratio. Use these formulas to determine the indicated term in the given sequence.

The 30th term of 1​, 4​, 7​, 10​,...

Answer 1

88

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=(a_2)/(a_1)=(4)/(1)=4`

`r_2=(a_3)/(a_2)=(7)/(4)`

`r_1\\eq 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.