Question

find a,b and c such that AP is ; a, 7, b, 23, c

Answer 1

Step-by-step explanation:

please mark has brainliest answer

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:a=-1}}}$

$\green{\tt{\therefore{Value\:of\:b=15}}}$

$\green{\tt{\therefore{Value\:of\:c=31}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies A.P = a,7,b,23,c \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Value \: of \: a = ? \\ \\ \tt: \implies Value \: of \: b = ? \\ \\ \tt: \implies Value \: of \: c= ?$

• According to given question :

$\tt\circ \: a_{1} = a \\ \\\tt\circ \: a_{2} = 7 \\ \\ \tt\circ \: a_{3} =b\\ \\\tt\circ \: a_{4} = 23 \\ \\ \tt\circ \: a_{5} = c\\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies a_{3} - a_{2} = a_{4} - a_{3} \\ \\ \tt: \implies b - 7 = 23 - b \\ \\ \tt: \implies 2b = 30 \\ \\ \green{\tt: \implies b = 15} \\ \\ \bold{Similarly : } \\ \tt: \implies a_{2} - a_{1} = a_{3} - a_{2} \\ \\ \tt: \implies 7 - a = 15 - 7 \\ \\ \tt: \implies a = 7 - 8 \\ \\ \green{\tt: \implies a = - 1} \\ \\ \bold{Similarly : } \\ \tt: \implies a_{4} - a_{3} = a_{5} - a_{4} \\ \\ \tt: \implies23 - 15 = c - 23 \\ \\ \tt: \implies c =8 + 23 \\ \\ \green{\tt: \implies c = 31}$