Question

The first term of a geometric sequence is 2, and the 4th term is 250. Find the 2 terms between the first and the 4th term.

Answer 1

second term: 10

third term: 50

Explanation:

The equation for any geometric sequence is
`a_(n) = a_(1) *r^(n-1)` where n is the term number you want to find,
`a_(1)` is the first term in the sequence, and
`r` is the common ratio. The equation for this sequence specifically uses 5 as its common ratio, so the equation is
`a_(n) =2*5^(n-1)`

`a_(1) = 2*5^(1-1)=2*5^(0) =2*1=2`

`a_(2) = 2*5^(2-1)=2*5^(1) =2*5=10`

`a_(3) = 2*5^(3-1)=2*5^(2) =2*25=50`

`a_(4) = 2*5^(4-1)=2*5^(3) =2*125=250`