Question

The nth term of an AP is given by an=7n+1 find the sum of the
first 30 terms ​

Answer 1

Answer:

sum of first 30 term is , 3285

Step-by-step explanation:

An = 7n + 1

let , n = 1

A1  = 7 + 1 = 8

n = 30  

A30 = 210 + 1 = 211

sum of first 30 term ,

S30 = 30/2 (8 + 211) = 15(219) = 3285

Answer 2

Step-by-step explanation:

Given that nth term of an arithmetic progression is Tn=7n+1

where n can be n=1,2,3,..

plugging n=1 gives first term

T1= 7*1+1=7+1=8

plugging n=2 gives second term

T2= 7*2+1=14+1=15

Common difference "d" can be found by difference of both terms

d=T2- T1= 15-8=7

Now we need to find sum of first 30 terms of arithmetic progression.

So we will use formula

S_n=\frac{n}{2}(2a+(n-1)d)S

n

=

2

n

(2a+(n−1)d)

where n=30, a=first term = 8, d=common difference = 7

plug those values

S_{30}=\frac{30}{2}(2*8+(30-1)*7)S

30

=

2

30

(2∗8+(30−1)∗7)

S_{30}=15(16+(29)*7)S

30

=15(16+(29)∗7)

S_{30}=15(16+203)S

30

=15(16+203)

S_{30}=15(219)S

30

=15(219)

S_{30}=3285S

30

=3285

Hence final answer is 3285.