Question

Find the 29th term of an A.P. whose 10th term is 20 and the 15th term is 50.

• A. 131
• B. 132
• C. 133
• D. 134

Answer 1

The correct option is D 134

Given that,
$a_{10}=20;a_{15}=50$
using nth term formula,
$a_n=a+(n-1)d$
$a_{10}=a+(10-1)d$
$20=a+9d$ ........ (1)
$a_{15}=a+(15-1)d$
$50=a+14d$ ........ (2)
subtracting equation (1) & (2), we get
$20=a+9d$
$50=a+14d$
-------------------
$-30=-5d$
$d=6$
put $d=6$ in equation (1)
$20=a+9\left(b\right)$
$20=a+54$
$a=-34$
$a_{29}=a+(29-1)d$
$=-34+\left(28\right)b$
$a_{29}=134$