Question

Find the solution for the problems based on nth term of the arithmetic progression. 1.a=2,a12=35 then find 'd'
2.a21=110,d=5 then find 'a' .


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Answer 1

$\huge{\boxed{\tt{\red{Question}}}}$

Find the solution for the problems based on nth term of the arithmetic progression.

a =2 , a12 = 35 then find 'd'

a21 = 110 , d = 5 then find 'a'

$\huge{\boxed{\rm{\blue{Answer}}}}$

Common difference of the arithmetic progression is $\large\purple{\texttt{3}}$

The first term of the arithmetic progression is $\large\purple{\texttt{10}}$

${\bigstar}\large{\boxed{\sf{\pink{1st}}}}$

We have 1st term $\large\purple{\texttt{a}}$ and 12th term $\large\purple{\texttt{t¹²}}$ of an A.P

$\large\pink{\texttt{Here we have}}$

$\large\red{\texttt{a = 2}}$

$\large\red{\texttt{t¹² = 35}}$

We have to find the common difference.

$\large{\texttt{We know that}}$

$\large\blue{\texttt{Formula}}$

t^n = a + ( n - 1 ) × d

Now let's carry on :]

t¹² = 2 + ( 12 - 1 ) × d

35 = 2 + 11d

35 - 2 = 11d

33 = 11d

d = 33/11

d = 3

D = 3

$\large\orange{\texttt{Hence the common difference between arithmetic progression is 3}}$

${\bigstar}\large{\boxed{\sf{\pink{2nd}}}}$

Given that 21st term (t²¹) nd common difference of the A.P

$\large\pink{\texttt{Here we have}}$

$\large\red{\texttt{t²¹ = 110}}$

$\large\red{\texttt{d = 5}}$

We have to find the 1st term.

$\large{\texttt{We know that}}$

$\large\blue{\texttt{Formula}}$

t^n = a + ( n - 1 ) × d

t²¹ = a + ( 21 - 1 ) × 5

110 = a + 20 × 5

110 = a + 100

110 - 100 = a

10 = a

a = 10

a = 10

$\large\orange{\texttt{Hence the first term of arithmetic progression is 10}}$

${\huge{\underline{\small{\mathbb{\pink{HOPE\:HELPS\:UH :)}}}}}}$

$\red{\tt{sωєєтcнαям♡~}}$

Answer 2

$\huge{\boxed{\rm{\blue{Answer}}}}$

Common difference of the arithmetic progression is $\large\purple{\texttt{3}}$

The first term of the arithmetic progression is $\large\purple{\texttt{10}}$

${\bigstar}\large{\boxed{\sf{\pink{1st}}}}$

We have 1st term $\large\purple{\texttt{a}}$a and 12th term $\large\purple{\texttt{t¹²}}$

$\large\pink{\texttt{Here we have}}$

$\large\red{\texttt{a = 2}}$

$\large\red{\texttt{t¹² = 35}}$

We have to find the common difference.

$\large{\texttt{We know that}}$

$\large\blue{\texttt{Formula}}$

t^n = a + ( n - 1 ) × d

Now let's carry on :]

t¹² = 2 + ( 12 - 1 ) × d

35 = 2 + 11d

35 - 2 = 11d

33 = 11d

d = 33/11

d = 3

D = 3

$\large\orange{\texttt{Hence the common difference between arithmetic progression is 3}}$

${\bigstar}\large{\boxed{\sf{\pink{2nd}}}}$

Given that 21st term (t²¹) nd common difference of the A.P

$\large\pink{\texttt{Here we have}}$

$\large\red{\texttt{t²¹ = 110}}$

$\large\red{\texttt{d = 5}}$

We have to find the 1st term.

$\large{\texttt{We know that}}$

$\large\blue{\texttt{Formula}}$

t^n = a + ( n - 1 ) × d

t²¹ = a + ( 21 - 1 ) × 5

110 = a + 20 × 5

110 = a + 100

110 - 100 = a

10 = a

a = 10

a = 10

$\large\orange{\texttt{Hence the first term of arithmetic progression is 10}}$