Question

the first term of an arithmetic sequence is -1 and the fifteenth term is 27 what is the comment difference?
a. 190
b. 195
c. 189
d. 200​

Answer 1

Answer :

common difference, d = 2

Step-by-step explanation :

$\underline{\underline{\bf Arithmetic \ Progression:}}$

•  It is the sequence of numbers such that the difference between any two successive numbers is constant.

•  In AP,

       a - first term

       d - common difference

       aₙ - nth term

       Sₙ - sum of n terms

•  General form of AP,

          a , a+d , a+2d , a+3d , ..........

•   Formulae :-

           nth term of AP,

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

         

         Sum of n terms in AP,

            $\boxed{\bf S_n=\frac{n}{2}[2a+(n-1)d]}$

_____________________________

Given,

• first term, a = -1
• fifteenth term, a₁₅ = 27

common difference, d = ?

=> a₁₅ = a + (15 - 1)d

    27 = -1 + 14d

    27 + 1 = 14d

    28 = 14d

    d = 28/14

    d = 2

∴ Common difference, d = 2

Answer 2

The common difference of AP is 2.

Step-by-step explanation:

We are given the first term(a) and fifteenth term(a15) of an AP are -1 and 27 respectively such as,

$a=-1$

$a15=27$

we have to find the common difference (d) of AP.

• Formula used,

$an=a+(n-1)*d$

where a is the first term of AP, d is the common difference and n is the term number of AP.

• Calculation for 'd'

By using formula we can write 15th term as,

$a15=27$    and $a=-1$

$a15=a+(15-1)*d$

$27=-1+(14)*d$

taking -1 o other side,

$27+1=14d$

$28=14d$

$d=\frac{28}{14}$

$d=2$

So the common difference of AP is 2.