Question

34.
The first term
of two A.P.s are equal and the ratios of their common
differences is 1 : 2. If the 7th term of first A.P. and 21th term
of
second A.P. are 23 and 125 respectively. Find two A.P.s.​

Answer 1

Hope it helps ........ .. .. .........

Answer 2

$Let \: First \:term \: of \: two \: A.P's = a$

$Ratio \: of \: common \: difference \:of \\A.P's = 1 : 2 \: ( given )$

$Let \: common \: difference \: first \:A.P = d$

$common \: difference \: f/secone \:A.P = 2d$

$\boxed { \pink { n^{th}\:term (a_{n}) = a + (n-1)d }}$

$7^{th}\: term \: of \: first \:A.P = 23$

$\implies a + 6d = 23\:--- (1)$

$21^{st}\: term \: of \: second \:A.P = 125$

$\implies a + 20\times (2d) = 125$

$\implies a + 40d = 125 \: ----(2)$

/* Subtract equation (1) from equation (2), we get */

$\implies 34d = 102$

/* On Dividing bothsides by 34 ,we get */

$\implies d = 3$

/* Substitute d = 3 ii n equation (1), we get */

$a + 6 \tines 3 = 23$

$\implies a = 23 - 18$

$\implies a = 5$

Therefore.,

Case 1 :

If a = 5 , common difference (d) = 3 then

First A.P:

5, 8, 11, 14, ....

Case 2 :

If a = 5 , common difference (2d) = 6 then

Second A.P:

5, 11, 17, ....

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