How do you write a rule for the nth term of the arithmetic sequence given #a_16=6, a_20=7#?

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Answer 1 · 2017-03-11T15:51:29

# a_n=1/4(n+8), or, 1/4n+2.#

In the Usual Notation, for an A.P., #a_n=a_1+(n-1)d...(0).#

#rArr a_16=a_1+15d, a_20=a_1+19d.#

#:. a_20-a_16=4d rArr 7-6=4d :. d=1/4.......(1).#

Next, #a_16=6, &, d=1/4 rArr a_1+15/4=6 rArr a_1=6-15/4=9/4...(2)#

Finally, #(0),(1) & (2) rArr a_n=9/4+1/4(n-1)=1/4(n+8), or,#

#a_n=1/4n+2.#

Enjoy Maths.!