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

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

idk

step-by-step explanation: