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'
​

Answer 1

Answer:

1. The common difference ( d ) of the arithmetic progression is 3.

2. The first term ( a ) of the arithmetic progression is 10.

Step-by-step-explanation:

1.

We have given the first term ( a ) and 12ᵗʰ term ( t₁₂ ) of an AP.

• a = 2
• t₁₂ = 35

We have to find the common difference ( d ).

Now, we know that,

tₙ = a + ( n - 1 ) * d - - [ Formula ]

⇒ t₁₂ = 2 + ( 12 - 1 ) * d

⇒ 35 = 2 + 11d

⇒ 35 - 2 = 11d

⇒ 11d = 33

⇒ d = 33 ÷ 11

⇒ d = 3

∴ The common difference ( d ) of the arithmetic progression is 3.

─────────────────────

2.

We have given the 21ˢᵗ term ( t₂₁ ) and common difference ( d ) of an AP.

• t₂₁ = 110
• d = 5

We have to find the first term ( a ).

Now, we know that,

tₙ = a + ( n - 1 ) * d - - [ Formula ]

⇒ t₂₁ = a + ( 21 - 1 ) * 5

⇒ 110 = a + 20 * 5

⇒ 110 = a + 100

⇒ 110 - 100 = a

⇒ a = 10

∴ The first term ( a ) of the arithmetic progression is 10.

Answer 2

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

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'

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

• 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

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

@Itzbeautyqueen23

Hope it's helpful

Thank you :)