# Thread: Solving a sequence question simultaneously

1. ## Solving a sequence question simultaneously

Hi

Question: I have to find the common difference and the first term when T8= 21 and T20= 105.

What I have done is state the rule : a + (n-1)d

Then came up with the equations a= 19x + 105 and a= 7x + 21
In y = mx +c form:

Then I obtained the common difference: 19d + 105 = 7d+ 21
19d +84 = 7d
12d+84
d = 7
And then I tried to get to get the first term by subtituting 7 into equation however this did not work:

I got the common difference correct but not the first term, can someone explain what I did incorrectly.

Help is greately respected and appreciated

Thank you

2. Originally Posted by atom360
Hi

Question: I have to find the common difference and the first term when T8= 21 and T20= 105.

What I have done is state the rule : a + (n-1)d

Then came up with the equations a= 19x + 105 and a= 7x + 21
In y = mx +c form:

Then I obtained the common difference: 19d + 105 = 7d+ 21
19d +84 = 7d
12d+84
d = 7
And then I tried to get to get the first term by subtituting 7 into equation however this did not work:

I got the common difference correct but not the first term, can someone explain what I did incorrectly.

Help is greately respected and appreciated

Thank you
n = 8: 21 = a + 7d .... (1)

n = 20: 105 = a + 19d .... (2)

(2) - (1): 84 = 12d => d = 7.

Substitute d = 7 into either (1) or (2) and solve for a.