Question

The 4th term of an ap is 1 and 11th term is 15. find its first term and nth term.​

Answer 1

Step-by-step explanation:

First term is -5 and nth term is 2n - 7

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Answer 2

The first term of AP is -5 and nth term is 2n-7.

Given:

• The 4th term of an AP is 1 and,
• 11th term is 15.

To find:

• Find its first term and nth term.

Solution:

Formula to be used:

General term of AP:

First term of AP is 'a' and common difference is 'd' then it's general term is given by$\bf a_n = a + (n - 1)d$

Step 1:

Write the equations in 'a' and 'd' from the given terms.

As,4th term is 1;

$a_4 = a + (4 - 1)d$

or

$\bf a + 3d = 1...eq1$

and

11th term is 15;

So,

$\bf a + 10d = 15...eq2$

Step 2:

Solve eq1 and eq2.

Subtract eq1-eq2

$a + 3d = 1 \\ a + 10d = 15 \\ ( - )( - ) \: \: ( - ) \\ - - - - - - - \\ - 7d = - 14 \\ - - - - - - -$

so,

$\bf d = 2$

Step 3:

Find the value of a.

Put the value of d in eq 1.

$a + 3(2) = 1$

or

$a = 1 - 6$

or

$\bf \red{ a = - 5}$

Thus,

The first term of A.P. is -5.

Step 4:

Find nth term.

Put the value of first term and common difference in general term.

$a_n = - 5 + (n - 1)2$

or

$a_n = - 5 + 2n - 2$

or

$\bf \red{a_n = - 7 + 2n}$

or

$\bf \red{a_n = 2n-7}$

Thus,

First term of AP is -5 and general term is 2n-7.

Learn more:

1) 26th, 11th and last term of an ap are 0, 3 and -1/5 respectively . find the common difference and the number of terms https://brainly.in/question/2643522

2) Write first four term of AP whose first term =-1.25 andthe common difference=-0.25 https://brainly.in/question/3458748