Question

2 different AP have same common difference the first term of the first AP is 2 more than 1st term of the 2nd AP if the 7th term of the first AP is 28 and 8th term of the second AP is 29 then find the two different AP

Answer 1

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Answer 2

$\huge{\mathtt{\purple{Solution⇢}}}$

${\underline{\mathtt{\green{GIVEN⇢}}}}$

1. The common difference of 2 A.P sequences is same .
2. 1st term of first A.P is 2 more than the 2nd A.P
3. 7th term of first A.P = 28
4. 8th term of second A.P = 29

${\underline{\mathtt{\green{To\:Find⇢}}}}$

➾ The two A.P sequences .

_________________________

➾The two sequences are A.P and a.p

➾Let's assume that the first term of A.P = x + 2

➾ And first term of a.p = x

—☆ We know that( a7 )th term of A.P = a + 6d

➾ 7th term of A.P = (x+2) + 6d

➾ x +2 + 6d = 28

➾ x + 6d = 26 ........ eq ( I )

➾ 8th term of a.p = x + 7d

➾ x +7d = 29

➾ x + 7d = 29 ........ eq ( II )

${\mathtt{\red{⇢\: Substracting \:eq \:I \:from \:eq\: II }}}$

➾ x + 7d - x - 6d = 29 - 26

${\boxed{\mathtt{\red{⇢ \: d\:=\: 3}}}}$

Putting the value of d in eq I

➾ x + 6(3) = 26

➾ x + 18 = 26

➾ x = 26 - 18

${\boxed{\mathtt{\red{⇢\: x \:= \:8 }}}}$

${\boxed{\mathtt{\red{⇢\: x\: + \: 2 \:= \:10}}}}$

So , the 2 A.P sequences are

➾ 10 , 13 , 16 , 19 ........

➾ 8 , 11 , 14 , 17 .........