Final answer:
To find the value of 'n' in an A.P., one uses the nth term and sum of terms formulas. With the given sum Sn=120, correct values for both t1 and t2 are needed to solve for n. The question contains ambiguities preventing an exact solution.
Step-by-step explanation:
To solve for the value of n in an arithmetic progression (A.P.) when given two terms t₁ and t₂ and the sum Sn, we use the formula for the nth term and the sum of the first n terms in an A.P.
The nth term of an A.P. is given by tₙ = a + (n - 1)d, where a is the first term and d is the common difference. The sum of the first n terms is Sn = n/2 * (2a + (n - 1)d).
In this case, we have an apparent ambiguity with two different t₁ values. Assuming there was a typo, and the correct first term t₁ is -5 and the common difference d can be found using the other given term t₂ = 45. With the given sum Sn = 120, we can substitute the known values into the Sn-formula and solve for n.
Unfortunately, to provide a complete step-by-step solution for n, correct values for t₁, t₂, and Sn are necessary. The presence of what seems to be typographical errors in the student's question prevents us from calculating an exact answer.