Given a_3=5a3=5 and a_5=1a5=1 in an arithmetic sequence, what is a_1a1 and dd?

2 Answers
Mar 22, 2018

"First Term " a_1 = 9, " Common Difference " d = -2First Term a1=9, Common Difference d=2

Explanation:

https://www.chilimath.com/lessons/intermediate-algebra/arithmetic-sequence-formula/https://www.chilimath.com/lessons/intermediate-algebra/arithmetic-sequence-formula/

Given a_3 = 5, a_5 = 1, " To find First Term " a_1, " common difference " da3=5,a5=1, To find First Term a1, common difference d

a_3 = a_1 + (3 - 1) * da3=a1+(31)d

a_1 + 2 d = 5, " Eqn 1 "a1+2d=5, Eqn 1

a_5 = a_1 + (5-1) * d a5=a1+(51)d

a_1 + 4d = 1, " Eqn 2 "a1+4d=1, Eqn 2

Solving equations (1), (2)

" Eqn 2 - Eqn 1 " Eqn 2 - Eqn 1

4d - 2d = 1 - 5 = -44d2d=15=4

2 d = -4 " or " d = -22d=4 or d=2

Substituting value of d in Eqn (1),

a_1 + 2 * -2 = 5a1+22=5

a_1 = 5 + 4 = 9a1=5+4=9

Mar 22, 2018

a_1= 9a1=9 and d=-2d=2.

Explanation:

U_n= a+(n-1)dUn=a+(n1)d

Now plug in the two equation in the question given and then solve simultaneously like shown below

a_3= a+(3-1)da3=a+(31)d

a_5= a+(5-1)da5=a+(51)d

Therefore

5= a+2d5=a+2d
1= a+4d1=a+4d


4= -2d4=2d

d=-2 d=2

Now plug one of the equations given in the question as you have already found out dd

U_3=a+(3-1)(-2)U3=a+(31)(2)

5=a+2(-2)5=a+2(2)

5=a -45=a4

5+4=a5+4=a

a=9a=9