Question

निम्नलिखित श्रेणियों के पद दर्शाए अनुसार ज्ञात कीजिए।
(a) 6, 10, 14,... का 28वाँ पद
(a) 10,8,6,... का 19वाँ पद
(1) 9,5,1,-3,... का 10वाँ पद
(iv) -6,-3,-1,1,... का nवाँ पद
(४) 80,77,74.....का 7वाँ पद
(vi) a + 2b,a-ba-4b,... का त्वाँ पद
fvil) 10.5.0,-5-10....का 10वाँ पद
Boad​

Answer 1

Step-by-step explanation:

10,8,6,......

A(19) = a+18d = 10 + 18*(-2)

= 10 - 36 = -26

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

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★ Solution :

(i) A.P : 6, 10, 14 .........

⟹ First term (a) = 6

⟹ Common Difference (d) = 4

We have o find 28th term of the A.P.

A.T.Q

We know the formula to find the term.

$\Large{\star{\underline{\boxed{\sf{A_{n} = a + (n - 1)d}}}}}$

As we have to find 28th term. So, Number of terms (n) will be 28.

(Putting Values)

$\sf{A_{28} = 6 + (28 - 1)4} \\ \\ \sf{A_{28} = 6 + 108} \\ \\ \sf{A_{28} = 114}$

$\large{\star{\underline{\boxed{\sf{A_{28} = 114}}}}}$

$\rule{200}{2}$

(ii) A.P :10, 8, 6 .........

⟹ First term (a) = 10

⟹ Common Difference (d) = -2

We have o find 19th term of the A.P.

A.T.Q

We know the formula to find the term.

$\Large{\star{\underline{\boxed{\sf{A_{n} = a + (n - 1)d}}}}}$

As we have to find 19th term. So, Number of terms (n) will be 19.

(Putting Values)

$\sf{A_{19} = 10 + (19 - 1)-2} \\ \\ \sf{A_{19} = 10 - 36} \\ \\ \sf{A_{19} = -26}$

$\large{\star{\underline{\boxed{\sf{A_{19} = -6}}}}}$

$\rule{200}{2}$

(iii) A.P : 9, 5, 1, -3........

⟹ First term (a) = 9

⟹ Common Difference (d) = -4

We have o find 10th term of the A.P.

A.T.Q

We know the formula to find the term.

$\Large{\star{\underline{\boxed{\sf{A_{n} = a + (n - 1)d}}}}}$

As we have to find 10th term. So, Number of terms (n) will be 1/.

(Putting Values)

$\sf{A_{10} = 9 + (10 - 1)-4} \\ \\ \sf{A_{10} = 9 - 36} \\ \\ \sf{A_{10} = -27}$

$\large{\star{\underline{\boxed{\sf{A_{10} = -27}}}}}$

$\rule{200}{2}$

(iv) A.P : -5, -3, -1, 1.........

⟹ First term (a) = -5

⟹ Common Difference (d) = 2

We have o find nth term of the A.P.

A.T.Q

We know the formula to find the term.

$\Large{\star{\underline{\boxed{\sf{A_{n} = a + (n - 1)d}}}}}$

As we have to find nth term. So, Number of terms (n) will be n.

(Putting Values)

$\sf{A_{n} = -5 + (n - 1)2} \\ \\ \sf{A_{n} = -5 + 2n - 2} \\ \\ \sf{A_{n} = 2n - 7}$

$\large{\star{\underline{\boxed{\sf{A_{n} = 2n - 7}}}}}$

$\rule{200}{2}$

(v) A.P : 80, 77, 74 .........

⟹ First term (a) = 80

⟹ Common Difference (d) = -3

We have o find 7th term of the A.P.

A.T.Q

We know the formula to find the term.

$\Large{\star{\underline{\boxed{\sf{A_{n} = a + (n - 1)d}}}}}$

As we have to find 7th term. So, Number of terms (n) will be 7.

(Putting Values)

$\sf{A_{7} = 80 + (7 - 1)-3} \\ \\ \sf{A_{7} = 80 - 18} \\ \\ \sf{A_{7} = 62}$

$\large{\star{\underline{\boxed{\sf{A_{7} = 62}}}}}$

$\rule{200}{2}$

(vii) A.P : 10, 5, 0, -5, -10.........

⟹ First term (a) = 10

⟹ Common Difference (d) = -5

We have o find 10th term of the A.P.

A.T.Q

We know the formula to find the term.

$\Large{\star{\underline{\boxed{\sf{A_{n} = a + (n - 1)d}}}}}$

As we have to find 10th term. So, Number of terms (n) will be qp.

(Putting Values)

$\sf{A_{10} = 10 + (10 - 1)-5} \\ \\ \sf{A_{10} = 10 - 45} \\ \\ \sf{A_{10} = -35}$

$\large{\star{\underline{\boxed{\sf{A_{10} = -35}}}}}$

$\rule{200}{4}$

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