Question

The first term of an AS is 10 and third term is 24 . what is its common difference ?​

Answer 1

Answer:

7

Step-by-step explanation:

Given,

First term of an A.P(a) = 10

Thrid term of an A.P(a₃) = 24

To Find :-

Common difference (d)

Formula Required :-

nth term of an A.P :-

aₙ = a + (n - 1)d

Solution :-

First term of an A.P = 10

→ a = 10

Third term of an A.P = 24

→ 24 = 10 + (3 - 1)d

24 = 10 + 2d

24 - 10 = 2d

14 = 2d

d = 14/2

d = 7

Common difference = d = 7

Answer 2

Answer:

Formula, we will be able to find the difference as follows:-

$\pink{\sf \: an = a1 + (n-1) × d}$

where

an = the last term in our required partition

a1 = the first term of the sequence

n = the number of terms in our required partition

d = the common difference between the terms of the sequence

So, to solve the problem we will identify the elements of the problem and assign each one to its proper definition in the formula as follows:-

an = 24

a1 = 10

n = 3

So, it’ll go like so

$\sf24 = 10 + (3–1) × d$

$\sf \: 24 = 10 + 2d$

$\sf \: 24 - 10 = 2d$

$\sf \: 14 = 2d$

$\sf \: 7 = d$

Hence, our common difference will be 7.

$\sf \: 10, 17, 24, 31, 38, 45 …$