The third term in an arithmetic sequence is 10 and the fifth term is 26. If the first term is a 1, what is an equation for the nth term of this sequence?

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Jim G. Share
May 30, 2016

Answer:

#a_n=8n-14#

Explanation:

The terms in the standard Arithmetic sequence are.

#a_1,a_1+d,a_1+2d,a_1+3d,.........,a_1+(n-1)d#

where #a_1" is the 1st term and d, the common difference"#

#a_1+(n-1)d" is the nth term"#

To obtain the nth term formula , we require to find #a_1" and d"#

we are given: #a_3=10" and " a_5=26#

#a_3=10rArra_1+2d=10rArra_1=10-2d.....(1)#

#a_5=26rArra_1+4d=26rArra_1=26-4d.......(2)#

equating (1) and (2): 10 -2d = 26 - 4d → d = 8

substitute d = 8 in (1) : #a_1=10-16=-6#

We now have d = 8 and #a_1=-6#

#rArra_n=-6+8(n-1)=8n-14#

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May 17, 2017

Answer:

Equation for nth term is #a_n = 8n-14. #

Explanation:

In this AP, the 3rd term is #10# and first term is #a_1#

In an AP #a_n = a_1+(n-1)d#

So by the formula: #" "a_3 = a_1+2d=10#

where (d is common difference)

Similarly, #a_5 = a_1+4d=26#

Solving these two equations by subtracting: #a_5 -a_3#
#a_1+4d=26#
#ul(a_1+2d=10)#
#" "2d = 16#

we get #d=8 and a_1=-6#

Now put these values in the formula:

#a_n=a_1+(n-1)d" :#

We get: #a_n = -6+(n-1)8#

#a_n=8n-14#
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