Q. 34.3( 139 Votes )

# For the following APs, write the first term and the common difference:

(i)

(ii)

(iii)

(iv)

Answer :

(i) Here, first term a = 3

Now,

The Common difference of the A.P. can be calculated as:

a_{4} – a_{3}

= - 3 – ( -1)

= - 3 + 1

= - 2

a_{3} – a_{2}

= - 1 – 1

= - 2

a_{2} – a_{1}

= 1 – 3

= - 2

Now, here a_{k+1} – a_{k} = - 2 for all values of k

Hence, first term = 3 and common difference = - 2

(ii) a_{4} – a_{3}

= 7 – 3

= 4

a_{3} – a_{2}

= 3 – (-1)

= 3 + 1

= 4

a_{2} – a_{1}

= - 1 – (-5)

= - 1 + 5

= 4

Now, here, a_{k+1} – a_{k} = 4 for all values of k

Therefore, first term = - 5 and common difference = 4

(iii) From the question,

a_{4} – a_{3}

=

a_{3} – a_{2}

=

a_{2} – a_{1}

=

Now, a_{k+1} – a_{k} = for all values of k

Therefore,

First term = 1/3 and common difference = 4/3

(iv) a_{4} – a_{3}

= 3.9 – 2.8

= 1.1

a_{3} – a_{2}

= 2.8 – 1.7

= 1.1

a_{2} – a_{1}

= 1.7 – 0.6

= 1.1

Now, here, a_{k+1} – a_{k} = 1.1 for all values of k

Therefore,

First term = 0.6 and common difference = 1.1

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