Question

6. How many terms are there in the following Arithmetic Progressions?

Answer 1

Hi ,

It is given that ,

i ) -1 , -5/6 , -2/3 ,...., 10/3 are in A.P

first term = a = -1

Common difference = a2 - a1

d = -5/6 - ( -1 )

= -5/6 + 1

= ( -5 + 6 )/6

= 1/6

last term ( an ) = 10/3

Let the number of terms = n

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We know that ,

a + ( n - 1 )d = an

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-1 + ( n - 1 )( 1/6 ) = 10/3

( n - 1 )/6 = 10/3 + 1

( n - 1 )/6 = ( 10 + 3 )/3

n - 1 = ( 6 × 13 )/3

n - 1 = 26

n = 27

Therefore ,

Number of terms in given A.P = n = 27

2 ) It is given that

7 , 13 , 19 , ....., 205 are in A.P

a = 7 ,

common difference = a2 - a1

d = 13 - 7

d = 6

Last term ( an ) = 205

Let number of terms = n

a + ( n - 1 )d = an

7 + ( n - 1 )6 = 205

( n - 1 )6 = 205 - 7

( n - 1 )6 = 198

n - 1 = 198/6

n - 1 = 33

n = 33 + 1

n = 34

Therefore ,

Number of terms in given A.P = 34

I hope this helps you.

: )