Given that x+1 , 3x-4 and 7x+3 are successive terms of an A.P. find the numerical value of x. If x+1 is the tenth term of the A.P.

Question

find the sum of the first eleven terms, the first twenty-eight terms and the terms from the twelfth term to the twenty-eighth term

Answer 1

What this problem tells you is:

x+1 = a₁ + 9d

3x-4 = a₁ + 10d

7x+3 = a₁ + 11d

where the arithmetic sequence in question is a_n = a₁ + (n-1)d

There are 3 unknowns and 3 equations.

Eliminate the a₁ by subtracting the first equation from the 2nd and the second from the third to get

(3x-4)-(x+1) = d

(7x+3)-(3x-4) = d

Set these 2 equations equal to each other and solve for x.

I got x = -6 which makes d=-17 and a₁ = 148