Question

4) If a=14 and a12=124, the value of d is

(a) 14 (b) 12 (c) 11 (d) 10​

Answer 1

Answer :

• d) 10

Given :

• a = 14
• a12 = 124

To find :

• d ( common difference)

Solution :

• For an AP , the nth term is given by :

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

$\therefore \tt a_{12} = a + ( 12 - 1)d$

124 = 14 + 11 d

124 - 14 = 11 d

110 = 11 d

d = 110 / 11

d = 10

___________________________

$\underline{\underline{\large{\mathfrak{ \purple{Arithmatic}\: \orange{progression : }}}}}$

Arithmetic progression is a series in mathematics in which each terms differs by a certain number called common difference.

A standard AP is in the form :

• AP = a , a + d , a + 2d , a + 3d....

The nth term of AP is given by :

• $\tt a_n = a + (n - 1) d$

The sum of the nth term of AP is given by :

• $\tt S_n = \dfrac{n}{2} [ 2a + ( n -1)d]$

Where

• $\tt a_n$ = nth term
• $\tt S_n$ = Sum of n terms
• a= first term
• n = number of terms
• d = common difference

Answer 2

$\huge{ \underline{ \underline{ \mathfrak{ \orange{answer \: : - }}}}}$

Concept:-

$\large\mathfrak \gray{lesson : } \: \mathfrak \red{arithmetic \: progressions}$

• An arthimetic progression is a list of numbers in which each term is obtained by adding a fixed numbers to the preceding term expect the first term.

• This fixed number is called the common difference of the A.P. Remember that it can be positive, negative or zero.

• General form of A.P is a, a+d, a+2d, a+3d,.....

$\iff \bf \: let \: us \: denote \: the \: first \: term \: as \: a_1 \: second \: term \: as \: a \:_2 \: and \: n \: th \: term \: as \: a \: _n$

Solution:-

Formula used:-

$\huge \sf \: a_n = a + (n - 1)d$

• a=14

• a12=124

• n=12

124=14+(12-1)d

124=14+(11)d

124-14=11d

110=11d

d=110/11

d=10