Question

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

Answer 1

1).
`T_(25)=119`

2).
`T_(1)=-23`

`T_(2)=-23+2=-21`

`T_(3)=-23+4=-19`

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

`T_(n)=a+(n-1)d`

Where
`T_(n)` 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.

`T_(25)=(-1)+(25-1)5`

= (-1) + 120

= 119

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

`T_(21)=17` and

`T_(50)=75`

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 =
`(58)/(29)=2`

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_(1)=-23`

`T_(2)=-23+2=-21`

`T_(3)=-23+4=-19`