Question

first term of an arithmetic sequence is 3 and the common difference is 4 write the algebraic form of this sequence write the sequence what is the tenth term of this sequence​

Answer 1

Answer:

4n+7

3,7,11

10TH TERM= COMMON DIFFERENCE/POSITION DIFFERENCE

                          11-3/3-1

                         = 8/2

                         =4

         4×10-1=39

10TH TERM=39                    

Step-by-step explanation:

Answer 2

Question:

First term of an Arithmetic sequence is 3 and the common difference is 4. Write the algebraic form of this sequence. What is the tenth term of this sequence.

Given:

• First term of Arithmetic progression is 3.
• Common difference is 4.

To Find:

• Algebraic form of this sequence.
• Tenth term of the sequence.

Concept:

Here, It is given the first term and common difference of Arithmetic progression. So, by given information we can find out the other terms and form a sequence. Secondly we have to find the Algebraic form of the sequence. For finding so, we have to find the nth term of Arithmetic progression in terms of it's first term and common difference.

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★ Formula Used:

$\mapsto\mathsf{{a}_{n}=a+(n-1)d}$

• $\bold{{a}_{n}}$ is General term of an Arithmetic progression.
• a is First term of Arithmetic progression.
• n is Term number.
• d is common difference.

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Solution:

Firstly, let's find the Sequence with first term as 3 and common difference as 4 .

$\rightarrow\sf{First\: term, a=3}$

$\rightarrow\sf{Second\: term, {a}_{2}=a+d=3+4=7}$

$\rightarrow\sf{Third\: term, {a}_{3}={a}_{2}+d=7+4=11}$

$\rightarrow\sf{Fourth\: term, {a}_{4}={a}_{3}+d=11+4=15}$

Hence, the required arithmetic progression is 3, 7, 11, 15…

Now, let's equate all values in Formula of nth term.

$\implies\sf{{a}_{n}=a+(n-1)d}$

$\implies\sf{{a}_{n}=3+(n-1)\times 4}$

$\implies\sf{{a}_{n}=3+4n-4}$

$\implies\bold{{a}_{n}=4n-1}$

This is the required algebraic form of sequence.

$\underline{\boxed{\mathtt{Algebraic\: form\: of\: sequence=\bold{\color{purple}{4n-1}}}}}$