we don't know the last term
hey infact we do know the last term,but we dont know the number of terms in the sequence and the first term in the sequence and hence cant find out the 4th term, correct ?
1) is sufficient for sure.
but 2 also give some info about last term, no. of terms and first term.
here it goes,
Since each term is three times the previous term, the series is a GP with common ratio 3.
let's say there are N+1 terms in the series and first term is a.
so, the second to last term is the nth term, which can be expressed as, a*(3^(n-1) ).
by statement 2, second-to-last-term is 310.
so, a*(3^(n-1) ) = 310 = 2*5*31.
since 310 does not have 3 as a factor, so a= 310 and 3^(n-1) must be 1
or , n-1 = 0
therefore n = 1
and n+1 = 2.
so, we get first term = 310 and total no of terms =2. and common ratio 3.
so we can get the other terms of the series.
BUT, here i have a doubt. if the total number of terms = 2, 4th term does not come into picture.
curious to know the OA.