Question

In a class the teacher asks every student to write an example of A.P. Two friends Geeta and Madhuri writes their progressions as -5, -2, 1,4, ... and 187, 184, 181, .... respectively. Now, the teacher asks various students of the class the following questions on these two progressions. Help students to find the answers of the questions. 

(i) Find the 34th term of the progression written by Madhuri.
(a) 286(b) 88(c) -99(d) 190 (ii)

Find the sum of common difference of the two progressions.
(a) 6(b) -6(c) 1(d) 0 (iii)

Find the 19th term of the progression written by Geeta.
(a) 49(b) 59(c) 52(d) 62 (iv)

Find the sum of first 10 terms of the progression written by Geeta.
(a) 85(b) 95(c) 110(d) 200 (v)

Which term of the two progressions will have the same value?
(a) 31(b) 33(c) 32(d) 30​

Answer 1

Step-by-step explanation:

Given: In a class the teacher asks every student to write an example of A.P.

Two friends Geeta and Madhuri writes their progressions as -5, -2, 1,4, ... and 187, 184, 181, .... respectively. Now, the teacher asks various students of the class the following questions on these two progressions.

To find: Help students to find the answers of the questions.

(i) Find the 34th term of the progression written by Madhuri.

(a) 286(b) 88(c) -99(d) 190

Sol: A.P. written by Madhuri is 187, 184, 181...

First term (a)= 187

Common difference (d)=184-187=-3

n=34

Formula for nth term:

$a_n = a + (n - 1)d$

$a_{34}= 187 + (34 - 1)( - 3)$

$a_{34}= 187 - 99$

$\bf a_{34}= 88$

Option b is correct.

(ii) Find the sum of common difference of the two progressions.

(a) 6(b) -6(c) 1(d) 0

Sol:

AP written by Geeta: -5, -2, 1,4...

Common difference $d_1=- 2 - ( - 5)$

$d_1= 3$

AP written by Madhuri is 187, 184, 181...

Common difference $d_2= -3$

Sum of both common differences=d1+d2

$= 3 - 3$

$\bf d_1-d_2= 0$

Option d is correct.

(iii) Find the 19th term of the progression written by Geeta.

(a) 49(b) 59(c) 52(d) 62

Sol:AP written by Geeta: -5, -2, 1,4...

First term (a)= -5

Common difference (d)= 3

n=19

$a_{19}= - 5 + (19 - 1)3$

$a_{19} = - 5 + 54$

$\bf a_{19} = 49$

Option a is correct.

(iv) Find the sum of first 10 terms of the progression written by Geeta.

(a) 85(b) 95(c) 110(d) 200

Sol: Sum of n terms of AP

$S_n = \frac{n}{2} (2a + (n - 1)d)$

n=10

a=-5

d=3

Put the values

$S_{10} = \frac{10}{2} (2 \times ( - 5) + (10 - 1)3)$

$S_{10} = 5 ( - 10 + 27)$

$S_{10} = 5 \times 17$

$\bf S_{10} = 85$

Option a is correct.

(v) Which term of the two progressions will have the same value?

(a) 31(b) 33(c) 32(d) 30

Sol:

Equate nth terms of both AP

nth term Geeta's AP=nth term of Madhuri's A.P.

$- 5 + 3(n - 1) = 187 - 3(n - 1)$

$- 5 + 3n - 3 = 187 - 3n + 3$

$6n = 187 + 5 + 3 + 3$

$6n = 198$

$\bf n = 33$

Option b is correct.

Final answer:

1) Option b is correct.

2) Option d is correct.

3) Option a is correct.

4) Option a is correct.

5) Option b is correct.

Hope it will help you.

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https://brainly.in/question/8420712

Answer 2

Step-by-step explanation:

Given: In a class the teacher asks every student to write an example of A.P.

Two friends Geeta and Madhuri writes their progressions as -5, -2, 1,4, ... and 187, 184, 181, .... respectively. Now, the teacher asks various students of the class the following questions on these two progressions.

To find: Help students to find the answers of the questions.

(i) Find the 34th term of the progression written by Madhuri.

(a) 286(b) 88(c) -99(d) 190

Sol: A.P. written by Madhuri is 187, 184, 181...

First term (a)= 187

Common difference (d)=184-187=-3

n=34

Formula for nth term:

\begin{gathered}a_n = a + (n - 1)d \\ \end{gathered}

a

n

=a+(n−1)d

\begin{gathered}a_{34}= 187 + (34 - 1)( - 3)\\ \end{gathered}

a

34

=187+(34−1)(−3)

\begin{gathered}a_{34}= 187 - 99\\ \end{gathered}

a

34

=187−99

\begin{gathered}\bf a_{34}= 88 \\ \end{gathered}

a

34

=88

Option b is correct.

(ii) Find the sum of common difference of the two progressions.

(a) 6(b) -6(c) 1(d) 0

Sol:

AP written by Geeta: -5, -2, 1,4...

Common difference \begin{gathered} d_1=- 2 - ( - 5) \\ \end{gathered}

d

1

=−2−(−5)

\begin{gathered} d_1= 3 \\ \end{gathered}

d

1

=3

AP written by Madhuri is 187, 184, 181...

Common difference \begin{gathered} d_2= -3 \\ \end{gathered}

d

2

=−3

Sum of both common differences=d1+d2

\begin{gathered} = 3 - 3 \\ \end{gathered}

=3−3

\begin{gathered} \bf d_1-d_2= 0 \\ \end{gathered}

d

1

−d

2

=0

Option d is correct.

(iii) Find the 19th term of the progression written by Geeta.

(a) 49(b) 59(c) 52(d) 62

Sol:AP written by Geeta: -5, -2, 1,4...

First term (a)= -5

Common difference (d)= 3

n=19