Question

The nth term of an arthemetic sequence is4n-2 find first term , common difference and 10th term

Answer 1

Answer:

first term = 3

common difference = -2

10th term = -15

Step-by-step explanation:

check the below image

Answer 2

$\sf\huge\blue{\underline{\underline{ Question : }}}$

The nth term of an Arithmetic Sequence is 4n-2 find first term , common difference and 10th term.

$\sf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• nth term of AP : 4n - 2

★ To find,

• First term(a).
• Common difference(d).
• 10th term.

★ Let,

$\bf\red{:\implies a_{n} = 4n - 2}$

◼ Substitute n = 1

$\bf\:\implies 4(1) - 2$

$\bf\:\implies 4 - 2$

$\bf\:\implies 2$

◼ Substitute n = 2

$\bf\:\implies 4(2) - 2$

$\bf\:\implies 8 - 2$

$\bf\:\implies 6$

◼ Substitute n = 3

$\bf\:\implies 4(3) - 2$

$\bf\:\implies 12 - 2$

$\bf\:\implies 10$

Hence, the AP series : 2,6,10.....

In the AP series, first term is 2.

$\underline{\boxed{\bf{\purple{\therefore First\:term(a) = 2}}}}\:\orange{\bigstar}$

How to find common difference (d)?

Let us take the AP series in the given question.

AP : 2,6,10....

Let,

$\tt\:\leadsto a_{1} = 2$

$\tt\:\leadsto a_{2} = 6$

$\tt\:\leadsto a_{3} = 10$

Common difference (d) : a2 - a1 = a3 - a2

$\tt\:\leadsto 6 - 2 = 10 - 6$

$\tt\:\leadsto 4 = 4$

↪ From the above we can see that the difference between the successive terms is same (constant) which is 4.

↪ so we can say that the given sequence is in A.P.

↪ If the 1st term and the common difference 'd' is given then we can make an arithmetic sequence.

★ To find 10th term,

• a = 2
• d = 4
• n = 10

By using nth term of AP formula, we can find the 10th term.

$\bf\red{:\implies a_{n} = a + (n - 1)d }$

• Substitute the values.

$\bf\:\leadsto a_{10} = 2 + (10 - 1)4$

$\bf\:\leadsto a_{10} = 2 + (9)4$

$\bf\:\leadsto a_{10} = 2 + 36$

$\bf\:\leadsto a_{10} = 38$

$\underline{\boxed{\bf{\purple{\therefore 10^{th} \: term\:of\:AP = 38.}}}}\:\orange{\bigstar}$

★ More Information :

$\boxed{\begin{minipage}{5 cm} AP Formulae \\ \\ : \implies a_{n} = a + (n - 1)d \\ \\ :\implies S_{n} = \frac{n}{2} [ 2a + (n - 1)d ] \end{minipage}}$

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