Question

write an AP whose a=4 and d=2•5.
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Answer 1

ANSWER :

AP = 4, 6.5, 9, 11.5, 14......

STEP-BY-STEP EXPLANATION :

GIVEN :-

a( first term) = 4

d( common difference) = 2.5

TO FIND :-

AP

FORMULA USED :-

First term (a) + common difference (d) = second term

a + 2d = third term

a + 3d = fourth term

a+ 4d = fifth term

SOLUTION :-

First term = a = 4

Common difference = d = 2.5

Second term = a2 = a+d = 4+2.5 = 6.5

Third term = a3 = a+2d = 4 + 2(2.5) = 4+ 5 = 9

Fourth term = a4 = a+3d =4 + 3(2.5) = 4 + 7.5 = 11.5

Fifth term = a5 = a + 4d = 4 + 4(2.5) = 4 + 10 = 14

VERIFICATION :-

As we know in an AP the common difference is constant everywhere in the AP. If a1 is the first term of an arithmetic sequence and d is the common difference, the sequence will be

An = (a1,a1+d,a1+2d,a1+3d,…). So, we can verify an AP by substraction second by the first term. If the common difference will be equal in each terms, then it will be proved that our answer is correct.

So,

AP = 4, 6.5, 9, 11.5, 14.....

a2 - a1 = 6.5 - 4 = 2.5

a3 - a2 = 9 - 6.5 = 2.5

a4 - a3 = 11.5 - 9 = 2.5

a5 - a4 = 14 - 11.5 = 2.5

As the difference between the terms results the same, then it is proved that our AP us correct.

Answer 2

a = 4 and d = 2.5

❥ Second term :- a2 = a + d

4 + 2.5 = 6.5

❥ Third term :- a3 = a + 2d

4 + 2 ( 2.5 ) = 4 + 5 = 9

❥ Fourth term :- a4 = a + 3d

4 + 3 ( 2.5 ) = 4 + 7.5 = 11.5

❥ Fifth term :- a5 = a + 4d

4 + 4 ( 2.5 ) = 4 + 10 = 14

Thus , the a.p is 4 , 6.5 , 9 , 11.5 , 14 , ......