For the following APs, write the first term and the common difference:
(i)
(ii)
(iii)
(iv)
(i) Here, first term a = 3
Now,
The Common difference of the A.P. can be calculated as:
a4 – a3
= - 3 – ( -1)
= - 3 + 1
= - 2
a3 – a2
= - 1 – 1
= - 2
a2 – a1
= 1 – 3
= - 2
Now, hereak+1 – ak = - 2 for all values of k
Hence, first term = 3 and common difference = - 2
(ii) a4 – a3
= 7 – 3
= 4
a3 – a2
= 3 – (-1)
= 3 + 1
= 4
a2 – a1
= - 1 – (-5)
= - 1 + 5
= 5
Now, here, ak+1 – ak = - 2 for all values of k
Therefore, first term = - 5 and common difference = 4
(iii) From the question,
a4 – a3
=
a3 – a2
=
a2 – a1
=
Now, ak+1 – ak = - 2 for all values of k
Therefore,
First term = 1/3 and common difference = 4/3
(iv) a4 – a3
= 3.9 – 2.8
= 1.1
a3 – a2
= 2.8 – 1.7
= 1.1
a2 – a1
= 1.7 – 0.6
= 1.1
Now, here, ak+1 – ak = - 2 for all values of k
Therefore,
First term = 0.6 and common difference = 1.1