Question

D Determine k such that 2/3,k,5/8
are the three consecutive terms of
an A.P​

Answer 1

2/3, k, 5/8 are three consecutive terms of an AP

_____________ [GIVEN]

Here..

$a_{1}$ = $\frac{2}{3}$

$a_{2}$ = k

$a_{3}$ = $\frac{5}{8}$

Now..

$a_{2}$ - $a_{1}$ = $a_{3}$ - $a_{2}$

=> k - $\frac{2}{3}$ = $\frac{5}{8}$ - k

$\frac{3k\:-\:2}{3}$ = $\frac{5\:-\:8k}{8}$

Cross-multiply them

=> 8(3k - 2) = 3(5 - 8k)

=> 24k - 16 = 15 - 24k

=> 24k + 24k = 15 + 16

=> 48k = 31

=> k = $\dfrac{31}{48}$

_______________________________

Answer 2

Answer:

k=31/48

Step-by-step explanation:

since they are successive terms their common difference will be equal* ignore first line in picture