Question

The sum of n terms of an ap is 7n2+9n fimd ap also find 18th term

Answer 1

Answer:

Series is 16,30,44,58......and so on

18th term is 254

Step-by-step explanation:

Given : The sum of n terms of an A.P is $S_n=7n^2+9n$

To find : A.P series and 18th term.

Solution : The sum of n terms of an A.P is $S_n=7n^2+9n$

To find the first term put n=1

$S_n=7n^2+9n$

$S_1=7(1)^2+9(1)$

$S_1=7+9=16$

Therefore, first term is 16

To find sum of two terms,

$S_n=7n^2+9n$

$S_2=7(2)^2+9(2)$

$S_2=28+18=46$

Now,

$S_2=a_1+a_2=46$

where $a_1=16$

$46=16+a_2$

$a_2=46-16=30$

So, we know first term = 16 and second term= 30

Therefore, we can find $d=a_2-a_1=30-16=14$

The series form with $a_1=16$ and d=14 is

→ Series is 16,30,44,58......and so on

Now, the 18th term is

$a_{n}=a_1+(n-1)d$

$a_{18}=16+(18-1)(14)$

$a_{18}=16+(17)(14)$

$a_{18}=16+238$

$a_{18}=254$

Therefore, 18th term is 254

Answer 2

Step-by-step explanation:

Answer:

Series is 16,30,44,58......and so on

18th term is 254

Step-by-step explanation:

Given : The sum of n terms of an A.P is S_n=7n^2+9nSn=7n2+9n

To find : A.P series and 18th term.

Solution : The sum of n terms of an A.P is S_n=7n^2+9nSn=7n2+9n

To find the first term put n=1

S_n=7n^2+9nSn=7n2+9n

S_1=7(1)^2+9(1)S1=7(1)2+9(1)

S_1=7+9=16S1=7+9=16

Therefore, first term is 16

To find sum of two terms,

S_n=7n^2+9nSn=7n2+9n

S_2=7(2)^2+9(2)S2=7(2)2+9(2)

S_2=28+18=46S2=28+18=46

Now,

S_2=a_1+a_2=46S2=a1+a2=46

where a_1=16a1=16

46=16+a_246=16+a2

a_2=46-16=30a2=46−16=30

So, we know first term = 16 and second term= 30

Therefore, we can find d=a_2-a_1=30-16=14d=a2−a1=30−16=14

The series form with a_1=16a1=16 and d=14 is

→ Series is 16,30,44,58......and so on

Now, the 18th term is

a_{n}=a_1+(n-1)dan=a1+(n−1)d

a_{18}=16+(18-1)(14)a18=16+(18−1)(14)

a_{18}=16+(17)(14)a18=16+(17)(14)

a_{18}=16+238a18=16+238

a_{18}=254a18=254

Therefore, 18th term is 254