Question

If the sum of n terms of an ap is 2n^2+5n then find the 4th term

Answer 1

Answer:

Sn=2n^2+5n

S1=2(1)^1+5(1)=7

S2=8+10=18

a1=7

a2=S2-S1

    =18-7

    =11

a=7

d=11-7=4

a4=a+3d

   =7+3(4)

   =19.

Answer 2

4th term of AP is 19.

Given:

• Sum of n terms of AP is $S_n=2 {n}^{2} + 5n$

To find:

• Find the 4th term of A.P.

Solution:

Concept to be used:

• Put values of n as 1,2,3.
• Find first term and common difference of AP.
• General term of AP $\bf a_n = a + (n - 1)d$

Step 1:

Put n= 1

$S_1 = 2( {1)}^{2} + 5(1)$

or

$\bf S_1 = 7$

If sum of 1 term is 7.

I.e. only 1 term is there.

So,

First term of AP is 7;

$\bf a = 7$

Step 2:

Put n= 2

$S_2 = 2( {2)}^{2} + 5(2)$

or

$S_2 = 8 + 10$

or

$\bf S_2 = 18$

Sum of first two terms is 18.

$a+a_2 = 18$

so,

$a_2 = 18 - 7$

or

$\bf a_2 = 11$

Second term is 11.

Step 3:

Find the common difference.

$d = a_2 - a$

or

$d = 11 - 7$

or

$\bf d = 4$

Step 4:

Find the 4th term.

a= 7

d= 4

n= 4

$a_4 = 7 + (4 - 1)4$

or

$a_4 = 7 + 12$

or

$\bf \red{a_4 = 19 }$

Thus,

4th term of AP is 19.

Learn more:

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