Question

14. if first term and common difference of an AP are 6 and 5 respectively. mnd its 13th term​

Answer 1

First term = a = 6
Common difference = d = 5
To find its 13 th term……
N = 13

Tn = a + (n -1) d
T13= 6 + (13 -1) 5
T 13 = 6+ 12 (5)
T13 = 6+ 60
T13 = 66


The 13th term is 66.




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Answer 2

Arithmetic Progression

We will use the concept of AP to solve the required problem.

AP - A sequence of numbers in which common difference between two consecutive terms is always same.

In an AP with first term $a$ and common diffence $d$, then nth term is given by,

$\boxed{\bf{\;T_n = a + (n - 1) d\;}}$

Solution:

Given that, the first term and common difference of an AP are 6 and 5 respectively. We are supposed to find its 13th term.

By substituting the given values in the formula, we get the following results:

$\implies T_{13} = 6 + (13 - 1) 5 \\\\\\ \implies T_{13} = 6 + 12 \times 5 \\\\\\ \implies T_{13} = 6 + 60 \\\\\\ \implies \boxed{\bf{T_{13} = 66}}$

Hence, the 13th term of the given AP is 66.

$\rule{200}{2}$

Extra Information

1. In an AP with first term $a$ and common diffence $d$, then nth term is given by,

$\boxed{\tt{\;T_n = a + (n - 1) d\;}}$

2. Let $a$ be the first term, $d$ be the common difference and $l$ be the last term of an AP. Then nth term from the end is given by,

$\boxed{\tt{\;l - (n - 1) d\;}}$

3. The sum of $n$ terms of an AP in which first term $a$, common diffence $d$ and last term $l$ is given by,

$\boxed{\tt{\;S_n = \dfrac{n}{2} (a + l)\;}}$