Question

write an As with common difference is 3 . find the 11th term.

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Answer 1

Answer:

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11th

Maths

Sequences and Series

Arithmetic Progression

Find the common difference ...

MATHS

Find the common difference and write the next four terms of each of the following arithmetic progression:

1,−2,−5,−8,......

November 22, 2019

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Devaprabha Mamillapalli

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ANSWER

Given A.P is

1,−2,−5,−8,....

hence the common difference is given by d=a

n+1

−a

n

by putting n=1 in above equation

d=a

2

−a

1

=(−2)−(1)

d=(−2−1)

d=−3

first term of this A.P is

a

1

=1

the nth term of this A.P is given by

a

n

=a

1

+(n−1)d

⟹a

n

=1+(n−1)(−3)

⟹a

n

=1−3n+3

⟹a

n

=4−3n….eq(1)

finding next four terms of A.P

1) for finding the 5th term of sequence (a

5

) put n=5 in eq(1)

⟹a

5

=4−3×5

⟹a

5

=4−15

⟹a

5

=−11

2) for finding the 6th term of sequence (a

6

) put n=6 in eq(1)

⟹a

6

=4−3×6

⟹a

6

=4−18

⟹a

6

=−14

Answer 2

Given:

The common difference of an AP is 3.

To Find:

the sequence of AP

the 11th term

Solution:

Common difference = 3

Let the first number be 1

Then, the A.P. is    1, 4, 7, 10,...

Now,

  $a_{n}$= a +(n-1)d

      the 11th term of A.P. is

  $a_{11}$= 1+(11-1) 3

       = 1+ (10)3

       = 31

So, $a_{11}$ = 31

Therefore, the 11th term is 31.