Question

Consider the AP: {7, 28, 49, 70, …}. Complete the following statements.
175 is the term of the AP.
1036 is the term of the AP.

Answer 1

➠Given A•P:-

7, 28 ,49, 70........

➠To find out:-

:-In which term does this number lie is AP 175 and 1056 is a term of the given AP.

➠Solution:-

Let a=first term of Arithematic progression

d=common difference of Arithematic progression

An=nth term of Arithematic progression

Now we have the given AP

7, 28, 49, 70.........

Here a=7 and d=28-7=21

Case:-1 (where An=175)

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Now An=a+(n-1)d

⇒ 175=7+(n-1)21

⇒ 175=7+21n-21

⇒ 175+14=21n

⇒ 189=21n

⇒ n=189/21

⇒ n=9

Hence, 175 is the 9th term of Arithematic progression.

Case:-2 (where An=1036)

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Now An=a+(n-1)d

⇒1036=7+(n-1)21

⇒ 1036=7+21n-21

⇒ 1036+14=21n

⇒ 1050=21n

⇒ n=1050/21

⇒ n=150

Hence, 1036 is also 150th term of Arithematic progression