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Home » 1. Show that the sequence defined by an = 5n – 7 is an A.P., find its common difference.
1. Show that the sequence defined by an = 5n – 7 is an A.P., find its common difference.
Arithmetic Progression | Arithmetic Progression | CBSE | Class 10 | Maths | Maths | RD Sharma
1. Show that the sequence defined by an = 5n – 7 is an A.P., find its common difference.

Solution:

Given, a<sub>n</sub> = 5n - 7

Now putting n = 1, 2, 3, 4 we get,

{{a}_{1}}=5[1]=5-7=-2

{{a}_{2=}}5[2]-7=10-7=3

{{a}_{3}}=5[3]-7=15-7=8

{{a}_{4}}=5[4]-7=20-7=13

We can see that,

{{a}_{2}}-{{\alpha }_{1}}=3-[-2]=5

{{a}_{3}}-{{a}_{{{2}_{{}}}}}=8-[-3]=5

{{a}_{4}}-{{a}_{3}}=13-[-8]=5

Since the difference between the terms is common, we can conclude that the given sequence defined by a<sub>n</sub> = 5n - 7 is an A.P with common difference 5.

i

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