Question

Tenth term of an arithmetic sequence is 20 and twentieth term is 10 1)What is the common difference 2)Find the first term 3) Write the algebraic form​

Answer 1

${\tt{\underline{Given :-}}}$

The tenth term of an arithmetic sequence is 20 and the twentieth term is 10

${\tt{\underline{Need\;to\;find:-}}}$

1)What is the common difference 2)Find the first term 3) Write the algebraic form​

${\tt{\underline{Answer :-}}}$

We've to first assume the common difference as d and the first term of the AP as a

We know the formula

aₙ = a + (n - 1)d

In the formula,

aₙ = Sum of the number of the term

a = First term of the AP

n = numbers of term

d = the common difference

Statement 1

$\tt a_{10}=a+(10-1)d$

$\tt 20=a+9d (1)$

Statement 2

$\tt a_{20}=a+(20-1)d$

$\tt 10=a+19d(2)$

Subtracting both equation

20 = a + 9d

10 = a + 19d

___________

$\tt 10 = (-10)d$

$\tt \dfrac{-10}{10}=d$

${\bf{\underline{-1=d}}}$

From 1

$\tt 20=a+9(-1)$

$\tt 20=a+(-9)$

$\sf 20+9=a$

$\tt 29=a$

So, your answers are

1) -1

2) 29

3) a + 9d & a + 19d