Question

Third term of an A.P. is 21 and the eighth term is 56.Find A.P. and also find its eleventh term.​

Answer 1

Answer:

49

Step-by-step explanation:

t3=a+2d=21

t8=a+7d=56

t8-t3=5d=56-21=35

d=7

t7=t8-d=56-7=49

Answer 2

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

$\green{\tt{\therefore{A.P=7,14,21,28,......}}}$

$\green{\tt{\therefore{11th\:term=77}}}$

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

$\green{\underline \bold{Given : }} \\ \tt: \implies Third \: term( a_{3})= 21 \\ \\ \tt: \implies Eight \: term( a_{8})= 56 \\ \\ \red{\underline \bold{To \: Find : }} \\ \tt: \implies A.P = ? \\ \\ \tt: \implies 11th \: term ( a_{11}) = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies a_{3} = a + 2d \\ \\ \tt: \implies 21 = a + 2d - - - - - (1) \\ \\ \bold{for \: 8th \: term : } \\ \tt: \implies a_{8} = a + 7d \\ \\ \tt: \implies 56 = a + 7d - - - - - (2) \\ \\ \text{On \: comparing \: (1) \: and \: (2)} \\ \green{\tt: \implies d = 7} \\ \\ \green{\tt: \implies a = 7} \\ \\ \tt \therefore A.P =7,14,21,28,..... \\ \\ \bold{For \: 11 \: th \: term : } \\ \tt: \implies a_{11} = a + 10d \\ \\ \tt: \implies a_{11} =7 + 10 \times 7 \\ \\ \tt: \implies a_{11} = 7 + 70 \\ \\ \green{\tt: \implies a_{11} =77}$