The 11th term of an progression is 25 and the sum of the first 4 terms is 49. The nth term of the progression is 49 1. Find the first term of the progression and the common difference
2. Find the value of n

For 1: The first term is 10 and the common difference is

For 2: The value of n is 27

Step-by-step explanation:

The n-th term of the progression is given as:

where,

is the first term, n is the number of terms and d is the common difference

The sum of n-th terms of the progression is given as:

where,

is the sum of nth terms

The 11th term of the progression:

              .......(1)

Sum of first 4 numbers:

             ......(2)

Forming equations:

                 ( × 8)

The equations become:

Solving above equations, we get:

Putting value in equation (1):

Hence, the first term is 10 and the common difference is

The nth term is given as:

Solving the above equation:

Hence, the value of n is 27

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