How do you write a rule for the nth term of the geometric term and then find #a_6# given #r=1/10, a_2=4#?

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Answer 1 · 2017-03-10T16:47:05

#T_6 = 1/2500 = 0.0004#

In a GP, each term is multiplied by the common ratio to get the next term in the sequence.

We do not have the first term, #a#, but we can find it from #T_2#

#T_2 = 4 = a xx 1/10#

#a = 4 xx 10 = 40#

#T_n = a r^(n-1)#

#T_n = 40 * (1/10)^(n-1)#

#T_6 = 40 *(1/10)^5#

#T-6 = 40 xx 1/10^5#

#T_6 = 1/2500 = 0.0004#