Question

Q-1- The first term of an AP is p and its common difference is q.find its 10th term.
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Answer 1

Answer:

The $10$th term of the AP whose first term is p and common difference q is

$a_{10} =p+9q$ .

Step-by-step explanation:

An AP ,Arithmetic Progression is a sequence of numbers which  either increases or decreases by a fixed number, called the common difference, and is denoted by d. It can be positive , negative , or zero. The general term of an AP is given by   $a_{n} =a+(n-1)d$ ,  

where a is the first term

d is the common difference

and n is the number of term.

In this question we asked to find the $10th$ term of an AP whose first term

$a=p$  and  $d=q$ .

Therefore   $a_{10} = a+(10-1)d$

                         $=p+9q$ .

Hence the answer.

thank you

Answer 2

Given

• a₁= p
• common difference= q

To find

• a₁₀

Concept

Arithmetic progression

Solution

We know that,

${\boxed{ \mathtt{a_{n}=a+(n−1)d}}}$

where

• a is the first term
• d is the common difference

$\sf{ \implies \: a_{10}=p+(10−1)q} \\ \\ \sf{ \implies \: a _ {10}=p+9q}$

Hence, 10th term is p+9q

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⭐More to know

Consider a A.P - a1 , a2, a3...an

• Common difference

d = a2 – a1 = a3 – a2 = ……. = an – an – 1

• The nth term of the AP

an = a + (n − 1) × d

• Sum of the nth term

S = n/2[2a + (n − 1) × d]