i know if the difference is the same, we use the formula a+(n-1)d but I have difficulty finding the nth term of a sequence where the differences are not the same. Please help i have my IGCSE exam next weak.
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I will give you some examples:
1): 1, 3, 6, 10,...
nth term, here difference increases by one in each step.
2nd term(3) up by '2' from previous term and 3rd term(6) up by '3' from previous term, so, nth term should up by 'n' from previous term.
i.e., nth term= (n-1)th term + n.
or, nth term= n-1+(n-2)th term + n.
and so on...
nth term= n*n - (1+2+3+...+n) = n*n - n(n+1)/2.
(2): 2, 4, 8, 16,...
nth term, each term is multiplied by 2 from previous term.
Let, 1st term= a
so, 2nd term= 2a
3rd term= 2*2a= 2^2a
...
nth term= 2^(n-1)a.
Remember there is no direct way to find nth term of any sequence. You have to analyse the sequence and try to connect the each term.
1): 1, 3, 6, 10,...
nth term, here difference increases by one in each step.
2nd term(3) up by '2' from previous term and 3rd term(6) up by '3' from previous term, so, nth term should up by 'n' from previous term.
i.e., nth term= (n-1)th term + n.
or, nth term= n-1+(n-2)th term + n.
and so on...
nth term= n*n - (1+2+3+...+n) = n*n - n(n+1)/2.
(2): 2, 4, 8, 16,...
nth term, each term is multiplied by 2 from previous term.
Let, 1st term= a
so, 2nd term= 2a
3rd term= 2*2a= 2^2a
...
nth term= 2^(n-1)a.
Remember there is no direct way to find nth term of any sequence. You have to analyse the sequence and try to connect the each term.
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You have the equaiton already !
a+(n-1)d
as n it yout nth term and the equation will give the nth value !
look at n=1 2 3 4 .........8
nth term a a+d a+2d a+3d........a+7d using the formulae above.
a+(n-1)d
as n it yout nth term and the equation will give the nth value !
look at n=1 2 3 4 .........8
nth term a a+d a+2d a+3d........a+7d using the formulae above.