Progression

Question

If second term of an AP is equal to the 9^th term of another AP. What will be the sum of 17 terms of second AP, as the sum of first 3 terms of first AP is given as 9.

A – 85; B – 102; C – 204; D – 51; E – Can’t be determined.

Answer 1

Given sum of first 3 terms of first AP=9

applying formula of sum of AP

9= $\frac{3}{2}*\left ( 2a_{1}+\left ( 2 \right )d_{1} \right )$

9=3* (a₁+d₁)

a₁+d₁=3

If second term of an AP is equal to the 9^th term of another

a₁+d₁=a₂₊8d₂

a₂₊8d₂=3

now

sum of 17 terms of second AP

S_n= $\frac{17}{2}*\left ( 2a_{2}+16d_{2} \right )$

S_n=17$\left ( a_{2}+8d_{2} \right )$

S_n=51

Answer option D                                                                                                                                          

Answer 2

if second term of an AP is equal to the 9^th term of another AP. What will be the sum of 17 terms of second AP, as the sum of first 3 terms of first AP is given as 9.

ans:

a9= a + 8d-----------------------------1

a2=a+d----------------------------------2

s17=? of 2nd ap series

s3= 3/2(2a+2d)= 3(a+d)=9

 a2 =a+d=3

s17=17/2(2a+16d)=17(a+8d)

where a9 = a2 as per condition 

therefore s17=17*(a+8d)=17*3=51

51 is the ans