Question

Find a,b,and c such that following numbers are in AP:a,7,b,23,c.

Answer 1

Answer:

Given:

• a, 7, b, 23 and c are in AP.

Find:

• Find value of a, b and c.

Calculations:

• (a, 7, b, 23 and c) are in AP.

Common difference:

• [(7 - a) = (b - 7) = (23 - b) = (c - 23)]

Taking terms of second and third:

⇒ b - 7 = 23 - b

⇒ 2b = 30

⇒ [b = 15]

Taking terms of first and second:

⇒ b - 7

⇒ [(7 - a) = (15 - 7)]

⇒ (7 - a) = 8

⇒ [a = - 1]

Taking terms of third and fourth:

⇒ [(23 - b) = (c - 23)]

⇒ [(23 - 15) = (c - 23)]

⇒ 8 = (c - 23)

⇒ (8 + 23) = 31

⇒ [c = 31]

Therefore, the vaule of a, b and c are = -1, 15 and 31.

Answer 2

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

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

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

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

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

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

• According to given question :

$\tt \circ \: a_{1} = a \\ \\ \tt \circ \: a_{2} = 7\\ \\\tt \circ \: a_{3} = b \\ \\\tt \circ \: a_{4} = 23 \\ \\\tt \circ \: a_{5} = c \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies 2 a_{2} = a_{1} + a_{3} \\ \\ \tt: \implies 2 \times 7 = a + b \\ \\ \tt: \implies a + b = 14 - - - - - (1) \\ \\ \bold{Similarly : } \\ \tt: \implies 2 a_{3} = a_{2} + a_{4} \\ \\ \tt: \implies 2b = 7 + 23 \\ \\ \tt: \implies b = \frac{30}{2} \\ \\ \green{\tt: \implies b = 15} \\ \\ \bold{Similarly : } \\ \tt: \implies 2 a_{4} = a_{3} + a_{5} \\ \\ \tt: \implies 2 \times 23 = b + c \\ \\ \tt: \implies 46 = 15 + c \\ \\ \tt: \implies c = 46 - 15 \\ \\ \green{\tt: \implies c = 31} \\ \\ \text{Putting \: value \: of \: b \: in \: (1)} \\ \tt: \implies a + 15 = 14 \\ \\ \tt: \implies a = 14 - 15 \\ \\ \green{\tt: \implies a = - 1}$