Question

if sum of first n term of an AP is 5n2-3n. find the AP and also find its 16 th term

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

The AP is 2, 12, 22,32,42...  and 16th term is 152.

Given:

• Sum of first n terms of an AP is $5n^{2} -3n$

To find:

• Find the AP and also find its 16th term.

Solution:

Formula/Concept to be used:

1. Sum of n terms of AP:$\bf S_n=\frac{n}{2} [2a+(n-1)d]$
2. General term of AP:$\bf a_n=a+(n-1)d$

Step 1:

It is given that

$S_n=5n^{2} -3n$

Find sum of 1 term; i.e put n=1

$S_1=5(1)^{2} -3(1)$

or

$S_1=2$

Sum of one term is 2. It is actually the first term of AP.

First term a:2

Find sum of 2 terms;ie put n=2

$S_2=5(2)^{2} -3(2)$

or

$S_2=20 -6=14$

Now, Sum of first two terms $a+a_1=14$

a=2,

so,

$\bf a_1=12$

By the same way find sum of first three terms.

put n=3

$S_3=5(3)^{2} -3(3)$

or

$S_3=36$

Find a2:

$a_2=S_3-S_2$

$\bf a_2=22$

Step 2:

Write AP.

First term of AP is 2.

Common difference d=12-2=10

22-12=10

Thus,

Common difference d=10

AP is 2, 12, 22,32,42...

Step 3:

Find the 16th term.

$a_{16}=2+(16-1)10$

or

$a_{16}=2+150$

or

$\bf a_{16}=152$

Thus,

AP is 2, 12, 22,32,42...

its 16th term is 152.

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