Find the twenty-fifth term of an arithmetic sequence if the first term is-1 and the common difference is 5. write the first three terms of an arithmetic sequence in which the twenty-first term is 17 and the fiftieth term is 75. 10. 11

1).

2).

Step-by-step explanation:

First term of an arithmetic sequence is (-1) and common difference is 5.

Then we have to find twenty fifth term of this arithmetic sequence.

Since explicit formula of an arithmetic sequence is represented by

Where represents nth term of the sequence.

a = first term

n = number of term

and d = common difference

Now we will find 25th term of this sequence.

= (-1) + 120

= 119

Similarly in second part of this question we have to find first three terms of an arithmetic sequence in which

and

Now from the explicit formula

17 = a + (21 - 1)d

17 = a + 20d   --------(1)

75 = a + (50 - 1)d

75 = a + 49d --------(2)

Now we subtract equation 1 from 2

75 - 17 = 49d - 20d

29d = 58

d =

By putting d = 2 in equation 1

17 = a + 20×2

17 = a + 40

a = 17 - 40

a = -23

Therefore, first three terms of this sequence will be

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680