Question

What is the sum of a 54-term arithmetic sequence where the first term is 6 and the last term is 377?

Answer 1

Sum of 54 terms in arithmetic sequence is 10341.

Solution:

In arithmetic series each successor number is obtained from predecessor number by adding or subtracting known as “common difference”.

Formula to find the sum of the 54 term arithmetic series: $\bold{S_{n}=\frac{n}{2}(a+l)}$

Given: Number of terms in the series is 54

First number in series = a =6

Last number in series = l = 377

Putting the values in above given formula we get $\bold{S_{54}=\frac{54}{2}(6+377)=10341}$

Answer 2

Answer:

$Sum\:of \: 54\:terms=10341$

Step-by-step explanation:

$Given \:in \:A.P\\first \:term (a)=6,\\last\:term(l)=377,\\and\: number \:of \: terms (n)=54\\Let\: common\: difference =d$

$we\:know \: that, \\last\:term = a+(n-1)d$

$\implies 377=6+(54-1)d$

$\implies 377-6 = 53d$

$\implies 371 = 53d$

$\implies \frac{371}{53} = d$

$\implies 7 = d$

$\implies d = 7$

$Now,\\Sum\:of \: n\:terms \:(S_{n})=\frac{n}{2}(a+l)$

$Now,\\Sum\:of \: 54\:terms \:(S_{54})=\frac{54}{2}(6+377)\\=27\times 383$

$=10341$

Therefore,

$Sum\:of \: 54\:terms=10341$

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