How do you find the first three terms of the arithmetic series a_1=17a1=17, a_n=197an=197, and S_n=2247Sn=2247?

2 Answers
Oct 28, 2017

First three terms are 17,26 and 3517,26and35

Explanation:

11st term is a_1=17 , a_n=197a1=17,an=197 , common difference is bb

And number of terms is nn.

Mid term is a_m=(17+197)/2=107 am=17+1972=107

Sum S_n+= a_m*n or 2247 = 107 * n :. n= 2247/107=21

a_n= a_1+(n-1)b or 197 = 17+ (21-1)b or 20b=180 or

b=180/20=9 :. a_2=a_1+b=17+9=26

a_3=a_1+2b=17+2*9=17+18=35

First three terms are 17,26 and 35 [Ans]

Oct 28, 2017

17,26,35...

Explanation:

An arithmetic sequence is the one in which the difference of the successive terms is the same

For example,

1,3,5,7.. is an arithmetic sequence because the common difference is 2. The symbol that i will use for the common difference here is d

Now lets solve the problem. For that we use the formula

color(green)(S_n=n((a_1+a_n)/2)

Where, S_n is the sum of the first n terms, a_1 is the first term and a_n is the n^(th) term. We already knew the values, so apply them

rarr2247=n((197+17)/2)

rarr2247=n(214)

color(green)(rArrn=21

Now we know that the 21^(st) term is 197

To find the common difference, we use

color(green)(a_n=a_1+(n-1)d

rarr197=17+(21-1)d

rarr180=20d

color(green)(rArrd=9

Now we have come to an end to the answer. We add 9 to each of the successive terms and we get

color(purple)(17,26,35....

Hope this helps!!! ☺