Math Help - Arithmetic Sequence

1. Arithmetic Sequence

In an arithmetic sequence, the 11th term is 53 and the sum ofof the 5th and 7th terms is 56. Find the first 3 terms of the sequence.

I'm trying to use the formula: tn= t1+(n-1)d but cant figure out where to get the numbers. Please step by step on how to get answer would be really helpful. Thanks

2. Re: Arithmetic Sequence

Using the given information, we obtain two equations in two unknowns:

$t_1+10d=53$

$(t_1+4d)+(t_1+6d)=56\,\therefore\,2t_1+10d=56$

If we subtract the first equation from the second, we will eliminate $d$ and we can solve for $t_1$. Then we can use this value to find $d$ from either of the original equations.

is t1 = 3?

4. Re: Arithmetic Sequence

Yes, so what is d?

5. Re: Arithmetic Sequence

oh sweet thanks so much! d=5 i got it now. everything fell into place

6. Re: Arithmetic Sequence

Yes, good work!