1. ## Arithmetic sequence

,IN the arithmetic sequence 17,a,b,c,41 what is the value of b?

2. Hello, Rimas!

You can baby-talk your way through this one . . .

In the arithmetic sequence: $17,\,a,\,b,\,c,\,41$, what is the value of $b$ ?

In an arithmetic sequence, the terms are "equally spaced".
Since the distance from the first to last is 24, they must be 6 units apart.

. . . . . . . . . $17\qquad\; a\qquad\;\: b \qquad\;\; c\qquad\;\, 41$
We have: . $- + - - + - - + - - + - - + -$
. . . . . . . . . . . $\underbrace{\qquad}_6\;\;\;\underbrace{\qquad}_6\; \;\;\underbrace{\qquad}_6\;\;\;\underbrace{\qquad} _6$

Got it?

3. Originally Posted by Rimas
,IN the arithmetic sequence 17,a,b,c,41 what is the value of b?
The 5th term, 41 is:
$17+4k=41$
Thus,
$4k=24$
Thus,
$k=6$
That means the 3rh term, b, is:
$b=17+2\cdot 6=17+12=29$