Question

The sum of 2nd and 4th term of an A.P. is 11 and the sum of the 5th and 10th terms is 20. Find the first three terms of the A.P.

• A. 3.5, 4.5 and 5.5
• B. 3, 4 and 5
• C. -3.5, 4 and 0
• D. 0, 3.5 and 2

Answer 1

The correct option is A 3.5, 4.5 and 5.5

Given that,
$a_2+a_4=11$ .........(1)
$a_5+a_{10}=20$ ...... (2)
we know that, $a_n=a+(n-1)d$
$a_2=a+(2-1)d;a_4=a+(4-1)d$
$a_2=a+d;a_4=a+3d$
similarly,
$a_5=a+(5-1)d;a_{10}=a+(10-1)d$
$a_5=a+4d;a_{10}=a+4d$
substitute the values of $a_2,a_5,a_4$ & $a_{10}$ in equation (1) & (2)
$\therefore a+d+a+3d=11$
$a+4d+a+9d=20$
$2a+4d=11$ ........... (3)
$2a+13d=20$ ........... (4)
(-) (-) (-)
-------------------
$-9d=-9$
$d=1$
put the value of d in equation (1)
$2a+4\left(1\right)=11$
$2a=11-4$
$2a=7$
$a=3.5$
$a_2=a+d=3.5+1=4.5$
$a_3=a_2+d=4.5+1=5.5$
$\therefore$ The first three terms of this A.P. are 3.5, 4.5 and 5.5