Math, asked by samiyatabassum, 6 months ago

find the fifthteen term of ap a=-23 d=4​

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Answered by vishal200444
0

Answer

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Answered by kunjika158
1

Answer:

The nth term or general term of an A.P is used to find terms arithmetic progression.

Let us consider an A.P. with first term as 'a' and the common difference as 'd'.

So the sequence is a, a + d, a + 2d, a + 3d, ... then,

1st term = a1 = a + (1 - 1)d

2nd term = a2 = a + d = a + (2 -1)d

3rd term = a3 = a + 2d = a + (3 -1)d

4th term = a4 = a + 3d = a + (4 -1)d

-

-

-

-

nth term = an = a + (n- 1)d

From the above we observe that the terms of A.P is given by

First term + ( term number - 1 ) (common difference)

Formula to find nth term of an A.P sequence is

an = a + ( n - 1) d

For example 15th term will be :

a15 = a + (15 - 1)d = a + 14d

Examples on Find terms arithmetic progression

1) Find the 19th and 24th terms of the A.P given by 21,16,11,6,1,...

Solution : We know that nth term of an A.P. is given by

an = a + (n - 1) d

To find a19,

n = 19, a = 21 and d = 16 - 21 = - 5

a19 = 21 + ( 19 -1 )(-5)

= 21 + 18 x(-5)

= 21 - 90

∴ a24 = - 69

To find a24,

n = 24, a = 21 and d = 16 - 21 = - 5

a24 = 21 + ( 24 -1 )(-5)

= 21 + 23 x(-5)

= 21 - 115

∴ a24 = - 94

2) Which term of the A.P. is 1, 6,11,16,... is 301 ?

Solution : The given sequence is in A.P.

So, a = 1 and d = 6 -1 = 5

Let us consider nth term as 301

an = a + (n - 1) d

301 = 1 + (n - 1)(5)

301 = 1 + 5n - 5

301 = -4 + 5n

301 + 4 = 5n

305 = 5n

305

5

=

5n

5

∴ n = 61

Thus 301 is 61st term.

3) Which term of the A.P. 5,15,25,... will be 130 more than its 31st term.

Solution: We have, a = 5 and d = 15 - 5 = 10

an = a + (n - 1)d

so, 31st term is

a31 = 5 + (31 - 1)(10)

a31 = 5 + 30 x 10

a31 = 305

Let the nth term of the given A.P. be 130 more than its 31st term.

an = 130 + a31

an = 130 + 305

an = 435

5 + (n - 1)(10) = 435

5 + 10n - 10 = 435

- 5 + 10n = 430

10n = 440

10n

10

=

440

10

∴ n = 44

Hence, 44th term of the given A.P is 130 more than its 31st term.

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