The first term of an Arithmetic progression is -12 and the last term is 40. The sum of the Arithmetic progression is 196. Find the nth term and common difference

Asked By Blessing On 07/01/2019 06:46

Answers

The sum of Arithmetic Progressiom formula goes as: S=[n/2](a+l) where a is your first term and l is your last term and s is the sum. We can substitute our numbers now: 196 = [n/2] (-12+40) 196 = [n/2] (28) 196 = 28n/2 Since we don't know n, we have to solve for it :) 392 = 28n N = 14 N is the amount of terms in the sequence. We have 14 terms here. To find the common difference, we use our arithmetic sequence forumla: a(n) = a(1) + (n-1)d We go ahead and substitute all we can :) 40 = -12 + (14-1)d Solve for d 52 = 13d D = 4 So we have 14 terms with a common difference of 4. Hope this helped :)
Answered On 07/01/2019 15:56


Hello Asked by Blessing You must know the formula Step 1 Find the n, how many numbers you have. Sn = (n/2)(a1 + an) 196 = (n/2)(-12+40) 196 = (n/2)(28) 196 = 14n n = 14 the nth term Step 2: Plug in into another formula an = a1 + (n-1) * d 40 = -12 + (14-1) * d 40 = -12 + 13d 52 = 13d 4 = d common difference
Answered On 07/04/2019 00:56