Given that, x-3,x+2 and x+7 are the first three consecutive terms of an AP find (a) the value of x (b) the first term and the common difference (c) the 10th term And (d) S6?

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Answer 1 · 2018-04-21T09:38:59

Kindly refer to the Explanation.

Part (a) :

#(x-3), (x+2) and (x+7)# are in AP.

# :. (x+2)# is the AM of #(x-3) and (x+7)#.

#:. (x+2)=1/2{(x-3)+(x+7)}=1/2(2x+4)=x+2#,

which is true #AA x in RR#.

# :. x in RR................................."[Ans. (a)]"#

Part (b) :

The first term, #t_1=a=(x-3).........................."[Ans. (b)]"#.

The common difference d

#=(x+2)-(x-3)=5......"[Ans.(b)]"#.

Part (c) :

#"The "10^(th)" term"=t_10=a+(10-1)d#,

#=a+9d#,

#=(x-3)+9xx5#.

# rArr t_10=(x+42)...................................."[Ans. (c)]"#.

Part (d) :

#S_n=n/2{2a+(n-1)d}#.

#:. S_6=6/2{2(x-3)+(6-1)xx5}#.

# rArr S_6=3(2x+19)#.