Given that nth term of an arithmetic progression is Tn=7-2n, find a)second term b)common difference ?? Help pls!!

2 Answers
NickTheTurtle
Jan 4, 2018

The second term of the arithmetic sequence is #color(blue)(3)#, and the common difference is #color(red)(-2)#.

Explanation:

It is given that the #n#th term of an arithmetic sequence is given as #T_n=7-2n#.

To find the second term, just substitute #n=2#:
#T_2=7-2*2=color(blue)(3)#

The common difference is defined as the number #T_(n+1)-T_n#, essentially the difference between a term and the previous term. We know that #T_(n+1)=7-2(n+1)=5-2n# and #T_n=7-2n#, so the common difference is
#T_(n+1)-T_n=(5-2n)-(7-2n)=color(red)(-2)#

Note that, since the common difference is negative, the arithmetic sequence is decreasing, i.e. the successive terms are smaller than the previous terms.

Jim G.
Jan 4, 2018

#a_2=3" and "d=-2#

Explanation:

#"to find the second term, substitute n = 2 into"#
#"the n th term formula"#

#rArra_2=7-(2xxcolor(red)(2))=7-4=3#

#"the common difference d is given as "#

#d=a_2-a_1=a_3-a_2=...... =a_n-a_(n-1)#

#"find the third term "#

#rArra_3=7-(2xxcolor(red)(3))=7-6=1#

#rArrd=a_3-a_2=1-3=-2#

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