Question

If4/5,a,2are three consecutive terms of A.P,find the value of a

Answer 1

Step-by-step explanation:

$\because \: \frac{4}{5} , \: a, \: 2 \: are \: consecutive \: \\ terms \: of \: AP \\ \\ \therefore \: their \: common \: differences \\ will \: be \: equal. \\ \\ \therefore \: a - \frac{4}{5} = 2 - a \\ \\ \therefore \: \frac{5a - 4}{5} = 2 - a \\ \\ \therefore \: 5a - 4= 5 \times (2 - a) \\ \\ \therefore \: 5a - 4= 10 - 5a \\ \\ \therefore \: 5a - 4= 10 - 5a \\ \\ 5a + 5a = 10 + 4 \\ \\ \therefore \: 10a = 14 \\ \\ \therefore \:a = \frac{14}{10} \\ \\ \huge \: \red{\boxed{ \therefore \:a = \frac{7}{5} }}$

Answer 2

$\Huge\bigstar\:\tt\underline\red{:ANSWER:}$

$\huge\mathscr\green{Given:-}$

${\implies}$$\frac{4}{5}$,${a,2......}$.

$\huge\mathscr\red{:First Term:}$

${\implies}$${a= -\frac{4}{5}}$

$\large\mathscr\blue{:Common difference:}$

${\implies}$${d=a2-a1=a3-a2}$

${\implies}$${a-\frac{4}{5}=2-a}$

${\implies}$${a+a=\frac{2}{1}+}$$\frac{4}{5}$

${\implies}$${2a=\frac{10+4}{5}}$

${\implies}$${a=\frac{14}{5×2}}$

${\huge{\boxed{\purple{\therefore{a=\frac{7}{5}}}}}}$.