1.

5th term of an AP is 5 times the first term and the 12th term exceeds the 7th term by 15, find the AP.​

Answer»

Answer:

3,6,9,12,.......

Step-by-step explanation:

given:

5th term of an AP is 5 times the FIRST term

12th term exceeds the 7th term by 15

to find:

find the AP

assumptions:

let a be the first term , and d be the COMMON difference

solution:

series is a,a+d,a+2d,a+3d,...............

clearly if you see second term you can tell that it is of the form a+(n-1)d

where n tells which term it is (EITHER 1st or 2nd ..)

so 5th term is a+(5-1)d = a+4d

given 5th term of an AP is 5 times the first term

so

a+4d = 5*a

==>4d = 4A

==> d = a            

12th term is a+ (12-1)d = a+11d

7th term is a+(7-1)d = a+6d

given 12th term exceeds the 7th term by 15

therefore

a+11d = (a+6d) + 15

===> 5d =15

==> d= 3

form both the UNDERLINED we can get

a =d = 3

so series is 3,6,9,12,.......


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