Question

find next two terms​

Answer 1

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

$\green{\tt{\therefore{Next\:two\:terms=5k+4\:and\:6k+5}}}$

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

$\green{\underline\bold{Given :}} \\ \tt: \implies A.P = k,2k + 1,3k + 2,4k + 3 \\ \\ \red{\underline\bold{To \: Find:}} \\ \tt: \implies Next \: two \: terms = ?$

• According to given question :

$\tt \circ \: a_{1} = k \: \: \: \: a_{2} = 2k + 1 \: \: \: \: a_{3} =3k + 2 \: \: \: \: a_{4}= 4k + 3\\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Common \: Difference = a_{2} - a_{1}\\ \\ \tt: \implies Common \: Difference = 2k + 1 - k \\ \\ \green{\tt: \implies Common \: Difference = k + 1} \\ \\ \bold{For \: 5th \: term(a_{5})} \\ \tt: \implies a_{5} = a_{1} + 4d \\ \\ \tt: \implies a_{5} =k + 4(k + 1) \\ \\ \tt: \implies a_{5} =k + 4k + 4 \\ \\ \green{\tt: \implies a_{5} =5k + 4} \\ \\ \bold{For \: 6th \: term( a_{6})} \\ \tt: \implies a_{6} = a_{1} + 5d \\ \\ \tt: \implies a_{6} =k + 5(k + 1) \\ \\ \tt: \implies a_{6} =k + 5k + 5 \\ \\ \green{\tt: \implies a_{6} =6k + 5} \\ \\ \green{\tt \therefore Next \: two \: terms \: are \: 5k + 4 \: and \: 6k + 5}$

Answer 2

Here is the answer

refer to the attachment