Question

Verify that each of the following is an $AP$, and then write its next three terms.

$0,\frac{1}{4},\frac{1}{2},\frac{3}{4}$,…

Answer 1

Arithemetic progression test:

Here,

$a_1=0$

$a_2=\frac{1}{4}$

$a_3=\frac{1}{2}$

$a_4=\frac{3}{4}$

$a_2–a_1=\frac{1}{4}–0=\frac{1}{4}$

$a_3–a_2=\frac{1}{2}–\frac{1}{4}=\frac{1}{4}$

$a_4–a_3=\frac{3}{4}–\frac{1}{2}=\frac{1}{4}$

Since, difference of successive terms are equal,

Hence, $0,\frac{1}{4},\frac{1}{2},\frac{3}{4}$……. is an $AP$with common difference $\frac{1}{4}$

Therefore, the next three terms can be determined as,

$\frac{3}{4}+\frac{1}{4},\frac{3}{4}+2\left(\frac{1}{4}\right),\frac{3}{4}+3\left(\frac{1}{4}\right)$

$1,\frac{5}{4},\frac{3}{2}$

Hence, next three terms of the A.P are$1,\frac{5}{4},\frac{3}{2}$.