Question 1047092
these are the formulas for an arithmetic sequence that i know.


<a href = "http://www.regentsprep.org/regents/math/algtrig/atp2/arithseq.htm" target = "_blank">http://www.regentsprep.org/regents/math/algtrig/atp2/arithseq.htm</a>


they should be the same as your formulas, except they use a rather than T and d rather than D.


converting their formulas to your nomenclature, i get:


Tn = T1 + (n-1) * D


Sn = n * (T1 + Tn) / 2


from the formulas and from what you are given, you don't need to find D, but i'll show you how to find it anyway after solving the problem.


you are given:


a) T1=7, Tn=79, n=8 


the formula for the sum of an arithmetic sequence is:


Sn = n * (T1 + Tn) / 2


you have what you need.


replace T1 with 7 and Tn with 79 and n with 8 and you have:


S8 = 8 * (7 + 79) / 2


solve for S8 to get S8 = 344


you didn't need D if you used the Sn formula.


you could solve for D as follows:


the formula for Tn is:


Tn = T1 + (n-1) * D


replace Tn with 79 and T1 with 7 and n with 8 and you get:


79 = 7 + (8-1) * D


simplify to get:


79 = 7 + 7 * D


subtract 7 from both sides of the equation to get:


72 = 7 * D


solve for D to get:


D = 72/7.


your formula of Tn = T1 + (n-1) * D becomes T8 = 7 + 7 * 72/7


solve for T8 to get T8 = 79.


value of D looks good.


you can also calculate each term from 1 to 8 and then add them up to see if the formula work as advertised.


you get:


T1 = 7 = 49/7
T2 = 7 + 1 * 72/7 = 121/7
T3 = 7 + 2 * 72/7 = 193/7
T4 = 7 + 3 * 72/7 = 265/7
T5 = 7 + 4 * 72/7 = 337/7
T6 = 7 + 5 * 72/7 = 409/7
T7 = 7 + 6 * 72/7 = 481/7
T8 = 7 + 7 * 72/7 = 553/7


add them up and you get a total of 2408/7 which is equal to 344.


the formulas look good.