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Home » 3. The general term of a sequence is given by an = -4n + 15. Is the sequence an A.P.? If so, find its 15th term and the common difference.
3. The general term of a sequence is given by an = -4n + 15. Is the sequence an A.P.? If so, find its 15th term and the common difference.
Arithmetic Progression | Arithmetic Progression | CBSE | Class 10 | Maths | Maths | RD Sharma
3. The general term of a sequence is given by an = -4n + 15. Is the sequence an A.P.? If so, find its 15th term and the common difference.

Solution:

Given, {{a}_{{{n}_{{}}}}}=-4n+15

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

{{a}_{1}}=-4[1]+15=-4+15=11

{{a}_{2}}=-4[2]+15=-8+15=7

{{a}_{3}}=-4[3]+15=-12+15=3   

{{a}_{4}}=-4[4]+15=-16+15=-1                 

We can see that,{{15}^{n}}

{{a}_{2}}-{{\alpha }_{1}}=7-[11]=-4

{{a}_{3}}-{{a}_{2}}=3-7=-4

{{a}_{4}}-{{a}_{3}}=-1-3=-4

Since the difference between the terms is common, we can conclude that the given sequence defined by {{a}_{n}}=-4n+15 is an A.P with common difference of -4.

Hence, the{{15}^{n}} term will be

{{a}_{15}}=-4[15]+15=-60+15=-45

i

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