Question

the first terms of two AP are equal and their common difference is 12 if seventh term is 23 and the 21st term is 25 find the two APS​

Answer 1

Correct Question:-

The first terms of two AP's are equal and their common difference is in the ratio 1 : 2. If the seventh term of first AP is 23 and 21st term of second AP is 125, Find the two AP's.

Answer:-

Let the first term of two AP's be "a" and the common difference of first AP be "d" then common difference of second AP will be "2d".

Given:

7th term of first AP = 23

→ a + (7 - 1)d = 23

→ a + 6d = 23

→ a = 23 - 6d -- equation (1)..

And,

21st term of second AP = 125

→ a + (21 - 1)2d = 125

→ a + 40d = 125

Now putting "a" from equation (1)

→ 23 - 6d + 40d = 125

→ 34d = 125 - 23

→ 34d = 102

→ d = 102/34

→ d = 3

→ Common difference of first AP = 3

→ Common difference of second AP = 2(3) = 6.

Substitute "d" value in equation (1).

→ a = 23 - 6d

→ a = 23 - 6(3)

→ a = 5

First term of two AP's = 5.

Now,

2nd term of first AP = a + (2 - 1)d

→ a(2) = 5 + 3 = 8

→ a(3) = 5 + 2(3) = 11.

Similarly,

2nd term of second AP = 5 + 6 = 11.

→ a(3) = 5 + 2(6) = 17.

Hence, Sequence of first AP is 5 , 8 , 11..... and Sequence of second AP is 5 , 11 , 17.....

Answer 2

Answer:

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