Question

for an AP the 12th term is 4 and the 20th term is -20. finf the nth term of the AP

Answer 1

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Answer 2

The nth term of A.P. is $\bf \red{a_n = 40 - 3n}$

Given:

• For an A.P. 12th term is 4 and
• 20th term is -20.

To find:

• find the nth term of the AP.

Solution:

Concept/formula to be used:

General term of A. P. is $\bf a_n = a + (n - 1)d$

here, a is first term, d is common difference.

Step 1:

It is given that, 12th term is 4

$a_{12} = a + 11d$

or

$\bf a + 11d = 4...eq1$

and 20th term is -20.

$\bf a + 19d = - 20...eq2$

Step 2:

Solve equations 1 and 2.

Subtract both equations.

$a + 11d = 4 \\ \: \: \: \: a + 19d = - 20 \\ ( - ) \: \: ( - ) \: \: ( + ) \\ - - - - - - - \\ - 8d = 24$

or

$d = \frac{ - 24}{8}$

or

$\bf d = - 3$

Find the value of a from eq1.

$a + 11( - 3) = 4$

or

$a - 33 = 4$

or

$\bf a = 37$

Step 3:

Put the value of a and d in general term.

$a_n = 37 + (n - 1)( - 3)$

or

$a_n = 37 - 3n + 3$

or

$a_n = 40 - 3n$

Thus,

nth term of A.P. is $\bf a_n = 40 - 3n$

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