Finding the Sum of an arithmetic series when the sum of the first two terms is given and the 20 th term is 93.

Question

$Sn$ = $\frac{n}{2}$ $[2a + d(n - 1)]$ {equation for working out the sum of an arithmetic series}

Question: The sum of the first two terms of an arithmetic series is 1. The 20th term is 93. Find the first term and the common difference of the series.

I have been told that I need to form linear equations and solve simultaneously but I don't know what the n is for sum of the first two terms part.

Thank You and Help is appreciated

Answer 1

The "one-and-a-halfth" term is $\frac12$, and the $20$th term is $93$. So the common difference is $(93-\frac12)/(20-1\frac12)$.

Answer 2

First "TWO terms" means $n=2$.

Answer 3

Let the Arithmetic Progression be $a,a+d,a+2d,...$

It is given that the sum of first two terms is $1$. $$\Longrightarrow a+(a+d)=1$$ $$\Longrightarrow 2a+d=1\ \ \ \ \ \ \ \ …(1)$$ Also given that the $20th$ term is $93$. Apply the formula for the $n^{th}$ term of AP. $$\Longrightarrow a+19d=93\ \ \ \ \ \ \ \ …(2)$$ Now, $(1)$ and $(2)$ are the linear equations which you have been told to solve simultaneously. After solving, you will get $$a=-2$$ $$d=5$$ Hope it helps:)