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 nth 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

Related questions
Impact of this question
6110 views around the world
You can reuse this answer
Creative Commons License