Question

Sum of the 10th term and 16th term of an arthematic squence is 78.calculate its13term

Answer 1

Answer:

$39$

Step-by-step explanation:

Let the first term of the Arithmetic Progression ($AP$) be $a$ and the difference between each subsequent term be $d$

We know that $n^{th}$ term of an $AP$ ($a_n$) = $a + (n-1)d$

⇒ $a_{10} = a + (10-1)d$

⇒ $a_{10} = a+9d$

⇒ $a_{16} = a + (16-1)d$

⇒ $a_{16} = a + 15d$

It is given that $a_{10} + a_{16} = 78$

⇒ $a + 9d + a + 15d = 78$

⇒ $2a + 24d = 78$

⇒ $2(a + 12d) = 78$

⇒ $a+12d = 39$

$a_{13} = a + (13-1)d = a+12d$

⇒ $a_{13} = 39$