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

Answer:

1). $T_{25}=119$

2). $T_{1}=-23$

$T_{2}=-23+2=-21$

$T_{3}=-23+4=-19$

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

$T_{n}=a+(n-1)d$

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 = $\frac{58}{29}=2$

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

$T_{1}=-23$

$T_{2}=-23+2=-21$

$T_{3}=-23+4=-19$