Q : 4         Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.

                 (ii)    \small 2,\frac{5}{2},3,\frac{7}{2},...

Answers (1)

Given series is
\small 2,\frac{5}{2},3,\frac{7}{2},...
Now,
first term to this series is = 2
Now,
a_1 = 2 \ \ and \ \ a_2 = \frac{5}{2} \ \ and \ \ a_3 = 3 \ \ and \ \ a_4 = \frac{7}{2}
a_2-a_1 = \frac{5}{2}-2 = \frac{5-4}{2}=\frac{1}{2}
a_3-a_2 = 3-\frac{5}{2} = \frac{6-5}{2} = \frac{1}{2}
a_4-a_3=\frac{7}{2}-3=\frac{7-6}{2} =\frac{1}{2}
We can clearly see that difference between terms are equal  and equal to \frac{1}{2}
Hence, given series is in AP
Now, next three terms are
a_5=a_4+d = \frac{7}{2}+\frac{1}{2} = \frac{8}{2}=4
a_6=a_5+d = 4+\frac{1}{2} = \frac{8+1}{2}=\frac{9}{2}
a_7=a_6+d =\frac{9}{2} +\frac{1}{2} = \frac{10}{2}=5

Therefore, next three terms of given series are  4,\frac{9}{2} ,5

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