Question

Find sum of arithmetic series where a1 = 7, n=31, nth a =127

Answer 1

Answer:

Sum of arithmetic series is $2077$

Step-by-step explanation:

We have $n$th term of arithmetic sequence

$a+(n-1)d$

Here

$a+(n-1)d=127\\\\7+(31-1)d=127\\\\d=\frac{120}{30} \\\\=4$

Sum of arithmetic sequence $=\frac{n}{2} (2a+(n-1)d)$

$=\frac{31}{2} (2\times7+(31-1)4)\\\\=\frac{31}{2} (14+120)\\\\=31\times67\\\\=2077$

Answer 2

Answer:

The sum of arithmetic series is 2077.

Step-by-step explanation:

Solution :

Here we have provided that :

• »» $\rm{a_1}$ = 1
• »» $\rm{n}$ = 31
• »» $\rm{a_n}$ = 127

We need to find :

• »» The sum of arithmetic series.

Here's the required formula to find the sum of arithmetic series :

$\longrightarrow{\pmb{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}$

Substituting all the given values in the formula to find the sum of arithmetic series :

${\longrightarrow{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}$

${\longrightarrow{\sf S = \dfrac{31}{2} \Big(7 + 127 \Big)}}$

${\longrightarrow{\sf S = \dfrac{31}{2} \Big(134 \Big)}}$

${\longrightarrow{\sf S = \dfrac{31}{2} \times 134 }}$

${\longrightarrow{\sf S = \dfrac{31}{\cancel{2}} \times \cancel{134 }}}$

${\longrightarrow{\sf S = 31 \times 67}}$

${\longrightarrow{\sf S = 2077}}$

$\star \: {\underline{\boxed{\sf{\red{S = 2077}}}}}$

Hence, the sum of arithmetic series is 2077.

$\rule{300}{1.5}$