Arithmetic sequences S1 and S2 have 5 terms each. If the first terms

Question

Arithmetic sequences  S_1  and  S_2  have 5 terms each. If the first terms of  S_1  and  S_2  are  a_1  and  a_2  respectively, and the difference between two consecutive terms of  S_2  is twice the difference between two consecutive terms of  S_1 , what is the ratio of the fifth term of  S_1 and the fifth term of  S_2 ?

(1)  a_1= 2a_2 
(2) The second term of both  S_1  and  S_2  is 3

stne · Answer

5th term of   s_1 : a_1 + 4x 
5th term of  s_2 :a_2 + 4 (2x)

We need :  \frac{ a_1 + 4x }{a_2 + 4 (2x)}  ... (I)

(1)  a_1= 2a_2

\frac{ 2a_2 + 4x }{a_2 + 4 (2x)}

\frac{2( a_2 + 2x )}{a_2 + 8x}

INSUFF.

(2) The second term of both  S_1  and  S_2  is 3

a_1 + x = 3  ...(II)
 a_2 + 2x = 3  ...(III)

a_1 - a_2 = x  ... ( II - III )

a_1 = x+ a_2  ... (IV)

Putting the value of  a_1  in ...(I)

\frac{ a_2+ 5x }{a_2 + 8x}

INSUFF.

1+2

From (1) We know  a_1 = 2a_2  
From (2) We know  a_1 = x+a_2 
 
So  2a_2 = x+a_2

a_2 = x

Therefore   a_1 = 2x

Putting all value in (I)

\frac{ 2x + 4x }{x + 8x}

\frac{6x}{9x} = \frac{6}{9}

SUFF.

Ans C

Hope it helped.

parthk24 · Answer

Bunuel , isn't B sufficient?

Assuming d 1  to be the common difference for S 1  and d 2  to be the common difference for S 2 , and as given in the question d 2 =2d 1

We know S 1 = a 1 , a 1 +d 1 , a 1 +2d 1 ....a 1 +4d 1 
S 2 = a 2 , a 2 +d 2 , a 2 +2d 2 ..a 2 +4d 2

As per B, 
a 1 +d 1 =3 -> (1)
and a 2 +d 2 =3 -> (2)

hence a 1 +d 1 =a 2 +d 2 
We know this means a 1 +d 1 =a 2 +2d 1 , rephrased as a 1 -a 2 =d 1 .

Now from (1) & (2), 
3-d 1 +3-d 2 =d 1 , rephrased as 3-d 1 +3-2d 1 =d 1 .
Therefore, 6=4d 1  or d 1 =1.5
Substitute in (1) & (2), and you get a 1 =3-1.5=1.5 and a 2 =3-3=0
Hence a 1 =1.5, d 1 =1.5 and a 2 =0, d 2 =3

The question asks us for the value of  \frac{a1+4d1}{a2+4d2}

We substitute the values above to get a complete answer i.e  \frac{7.5}{12} 
Hence the statement is sufficient.

Please let me know if there is anything missing or done incorrectly.

adconsectetur · Answer

a1-a2 = d1.

Now substitute a1 = 3- d1 and a2 as 3-d2

3-d1. - (3-d2)..

you have written it as 3-d1 + 3-d2

Hope it helps

Arithmetic sequences S1 and S2 have 5 terms each. If the first terms

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Arithmetic sequences S1 and S2 have 5 terms each. If the first terms

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