Math, asked by zxdestroyer14, 5 hours ago

4. A sequence (an) is given by the formula an = 10 – 3n, is an AP, find the common difference of the sequence.​

Answers

Answered by Anonymous
20

Provided that: A sequence (AP) is given by the formula {\sf{a_n \: = 10 - 3n}} , is it an AP!? Find the common difference of the sequence.

Knowledge required:

→ d = 2nd term - 1st term

→ d = 4th term - 3rd term

Required solution:

~ Firstly let us put n as 1

{\sf{:\implies a_n \: = 10 - 3n}}

{\sf{:\implies a_1 \: = 10 - 3(1)}}

{\sf{:\implies a_1 \: = 10 - 3}}

{\pmb{\sf{:\implies a_1 \: = 7}}}

~ Now let us put n as 2

{\sf{:\implies a_n \: = 10 - 3n}}

{\sf{:\implies a_2 \: = 10 - 3(2)}}

{\sf{:\implies a_2 \: = 10 - 6}}

{\pmb{\sf{:\implies a_2 \: = 4}}}

~ Now let's put n as 3

{\sf{:\implies a_n \: = 10 - 3n}}

{\sf{:\implies a_3 \: = 10 - 3(3)}}

{\sf{:\implies a_3 \: = 10 - 9}}

{\pmb{\sf{:\implies a_3 \: = 1}}}

~ Now let us put n as 4

{\sf{:\implies a_4 \: = 10 - 3n}}

{\sf{:\implies a_4 \: = 10 - 3(4)}}

{\sf{:\implies a_4 \: = 10 - 12}}

{\pmb{\sf{:\implies a_4 \: = -2}}}

Therefore, series be like 7, 4, 1, -2...

~ Now let us find out the common difference by using suitable formula!

→ d = 2nd term - 1st term

→ d = 4 - 7

→ d = -3

___________________________

→ d = 4th term - 3rd term

→ d = -2 - 1

→ d = -3

  • Henceforth, d are same in both the conditions, therefore, the series in an arithmetic series. And here the common difference is -3
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