Question

The Algebra of an arithmetic sequence 6n+5 .Find the sum of first 20 term of the sequence ​

Answer 1

Answer:

$\large\mathrm\blue{Given:}$

The Algebra of an arithmetic sequence

$\fbox{\large\mathrm{6n + 5}}\:$

$\mathrm {a_1\: = \: First \: Term } \\ \\ \mathrm{a_2 \: = \: Second Term} \\ \\ \mathrm{ d\: = \: Common \: Difference}$

$\large\mathrm\blue{To\: find:}$

ᴛʜᴇ sᴜᴍ ᴏғ ғɪʀsᴛ 20 term ᴏғ ᴛʜᴇ sᴇǫᴜᴇɴᴄᴇ.

$\large\mathrm\blue{Solution}$

From the given data,

$\huge\fbox{\mathrm{ a_n = 6n + 5}}$

We need to find :

$\huge\mathrm\purple{a_1 = ? } \:$

$\mathrm{a_n= 6(n) + 5} \\ \\ \implies \mathrm{a_1 = 6 + 5 } \\ \\ \implies \large\fbox{\mathrm{a_1 = 11}} \:$

$\huge\mathrm\purple{a_2= ? }\:$

$\mathrm{a_n = 6(n) +5} \\ \\ \implies \mathrm{a_2= 6(2) +5 } \\ \\ \implies \large\fbox{a_2 = 17} \:$

$\large\mathrm\purple{d \: = ? } \:$

$\mathrm{ d = a_2 - a_1} \:$

$\implies \mathrm{ 17 - 11 } \\ \\ \implies \large\fbox {d = 6} \:$

Let's find the sum of first 20 terms in the sequence :

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

$\large\mathrm{S_20 = \frac{20}{2} [ 2(11) + (20-1) (6)]} </p><p></p><p>\\ \\ \implies \large\mathrm{ 10 [ 22)+ (19) 6]} \:$

$\implies \large\mathrm{220 + 114} \\ \\ \implies \large\fbox{334} \:$

Hence the sum of first 20 terms of the sequence is 334.

$\huge\mathfrak\pink{verified} \:$