How to know the (first term) in arithmetic sequence?

Question

I have an arithmetic sequence and all what I know is the following: The sum of the first 15 terms = 165 The common difference 2

That is:

$sum = 165$

$d = 2$

$n = 15$

$a = ?$

I need to know the first term that is $a_1$

My attempt:

To find the nth term in arithmetic sequence we use the formula $a_n = a+(n-1)d$ we already know the values of $n$ and $d$ and so I substitute:

$a_{15} = a + (15-1)(2)$

$a_{15} = a + 28$

I'm stuck here...

Answer 1

If $$S_n= 165,d=2,n=15,a_1 = ?$$ from $$S_n=\frac{n}{2}(2a_1+(n-1)d)$$ we have $$\frac{15}{2}(2a_1+(15-1)2)=165$$

$$a_1+14=11$$ $$a_1=-3$$

Answer 2

By the formula of sum of an AS, you know that

$$164=S_{15}=\frac{15}2\left(2a_1+14\cdot2\right)$$

Well, just find out what $\;a_1\;$ is from the above.

Answer 3

I have a question that i dont know how to solve it, The sum of the first 10 terms of a sequence is 275. If the common difference is -5, find the 1st term and tenth term.