Find the first term and common difference for the A . P . 1 4 , 3 4 , 5 4 , 7 4 . . . . .

The given A . P . is 1 4 , 3 4 , 5 4 , 7 4 . . . . . We know that, in A . P . t 1 is the first term of the sequence and common difference d is difference between two consecutive terms, that is d = t n + 1 - t n Now, from the given sequence first term t 1 = 1 4 Common difference d = t 2 - t 1 = 3 4 - 1 4 = 3 - 1 4 = 1 2 Hence, the first term and the common difference for the given A . P . is 1 4 and 1 2 .

Is - 1 5 , - 1 5 , - 1 5 , . . . . . . an A . P . if so then find the common difference.

Given: - 1 5 , - 1 5 , - 1 5 , . . . . . . We need to check whether the given sequence is an A . P . Here, in the given sequence first term t 1 = - 1 5 , second term t 2 = - 1 5 and so on... We know that, common difference d = t n + 1 - t n Now, t 2 - t 1 = - 1 5 - - 1 5 = - 1 5 + 1 5 = 0 and t 3 - t 2 = - 1 5 - - 1 5 = - 1 5 + 1 5 = 0 Here, difference between consecutive terms is same. Therefore, yes the given sequence is an A . P . and the common difference is 0 .

E M B I B E

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Arithmetic Progression>Exercise

Exercise

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