Question

5th term of an AP is 26 and 10th term is 51. The 15th term is :

• A. 60
• B. 76
• C. 55
• D. 72

Answer 1

Answer: (B)

76

Given 5th term and 10th term of an AP are 26 and 51 respectively.
$a+4d=26a+9d=51$
Solving the above equations, we get
$-25=-5d⟹d=5$
Plugging in d = 5 in either of above two equations, we get
$26=a+4\left(5\right)⟹26=a+20⟹a=6$
To find the 15th term,
$t_{15}=a+(n-1)d⟹t_{15}=6+5(15-1)⟹t_{15}=76$.
The $15th$ term is $76$.