Sequences & Series · Ordinary Level
Consecutive Terms
Ordinary Level · Class 4 · Tap NEXT to begin
Section 1 of 1
Three Terms in a Row
Equal gaps
If three terms are consecutive in an arithmetic sequence, the gaps are equal: $T_2 - T_1 = T_3 - T_2$. (The same as saying the middle term is the average of the outer two.)
Worked example — find x
$3$, $2x+1$, $9$ are three consecutive terms of an arithmetic sequence. Find $x$.
Middle $=$ average: $2x + 1 = \dfrac{3 + 9}{2} = 6$
$2x = 5 \Rightarrow x = 2.5$
(Check with gaps: $2x+1-3 = 9-(2x+1) \Rightarrow 2x-2 = 8-2x \Rightarrow 4x = 10$, same answer.)
$x = 2.5$
Worked example — a two-term expression
$3$, $2x+5$, $x+12$ are three consecutive arithmetic terms. Find $x$.
$T_2 - T_1 = T_3 - T_2$: $(2x+5) - 3 = (x+12) - (2x+5)$
$2x + 2 = -x + 7$
$3x = 5 \Rightarrow x = \tfrac{5}{3}$
$x = \tfrac{5}{3}$
You try
$3$, $2x-1$, $x+5$ are three consecutive arithmetic terms. Find $x$.
$(2x-1) - 3 = (x+5) - (2x-1)$.
$2x - 4 = -x + 6$
$3x = 10 \Rightarrow x = \tfrac{10}{3}$
$x = \tfrac{10}{3}$
You try
$2k-1$, $2k+1$, $3k$ are three consecutive arithmetic terms. Find $k$.
$(2k+1) - (2k-1) = 3k - (2k+1)$.
$2 = k - 1$
$k = 3$
$k = 3$
That’s Class 4.
Consecutive terms have equal gaps: $T_2 - T_1 = T_3 - T_2$. Class 5: finding $a$ and $d$ from two given terms.