Question

the sum of AP 2,5,8..... up to 50 terms is a)3557 b)3775 c)3757 d)3575​

Answer 1

$\huge {\boxed {\mathbb {QUESTION}}}$

The sum of AP 2,5,8..... up to 50 terms is

a)3557 b)3775 c)3757 d)3575

$\huge {\boxed {\mathbb {ANSWER}}}$

${\boxed {\mathbb {GIVEN}}}$

$2,5,8..... up to 50 terms$

$a=2,d=3,n=50$

${\boxed {\mathbb {TO\:PROVE}}}$

$Sum\: of \:50 \:terms\: of\: the\: AP$

$Formula=\\S_n=\frac{n}{2}[2a+(n-1)d]$

$Substitute\: the\: values$

$\implies S_50=\frac{50}{2}[2(2)+(50-1)3]$

$\implies S_50=25[4+(49)3]$

$\implies S_50=25[4+147]$

$\implies S_50=25[151]$

$\implies {\boxed {\boxed {S_50=3775}}}$

$\huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

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$\huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$Formulas$

$a_n=a+(n-1)d$

$S_n=\frac{n}{2}[2a+(n-1)d]$

$S_n=\frac{n}{2}[a+a_n]$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$

Answer 2

We are given an AP series

Let

$a0 = 2 \\ a1 = 5 \\ a2 = 8 \\ ....upto \: 50 \: terms$

We need to calculate the sum of 50 terms of the given AP series.

The formula to calculate the sum of n terms of AP series is

$sn = n \div 2(2a + (n - 1)d)$

Here

$a = \: first \: term \: of \: the \: sequence \\ = 2 \\ d = common \: difference = a1 - a0 \\ = 5 - 2 \\ = 3 \\ n = number \: of \: terms = 50$

By substituting the above values in the equation we get

$sn = 50 \div 2(2 \times 2 + (50 - 1)3) \\ = 25(4 + 49(3)) \\ = 25(4 + 147) \\ = 25(151) \\ = 3775$

Therefore, sum of the given AP series upto 50 terms is

$3775$

Hence, the correct option is b

#SPJ2