# 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

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

Answered On 07/04/2019 00:56

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