Question

if the nth term of an AP is (5A − 3), find the sum of first 20 terms of the AP

using the formula.​

Answer 1

/* There is a mistake in the question. It may be like this */

$n^{th} \:term \: of \: A.P : a_{n} = 5n-3$

$i) If \: n = 1 \: then \: a_{1} = 5\times 1 - 3 \\= 5 - 3 \\= 2$

$ii) If \: n = 2 \: then \: a_{2} = 5\times 2 - 3 \\= 10 - 3 \\= 7$

$iii) If \: n = 3 \: then \: a_{3} = 5\times 3 - 3 \\= 15 - 3 \\= 12$

$First \term (a) = 2$

$Common \: differnce (d) = a_{3} - a_{2} \\= 12 - 7 \\= 5$

$\boxed { \pink { Sum \: of \:n \:terms (S_{n}) = \frac{n}{2}[2a+(n-1)d] }}$

$Now, Sum \:of \: 20 \: terms S_{20} \\= \frac{20}{2}[ 2 \times 2 + (20-1)5 ] \\= 10[ 4+19 \times 5 ] \\= 10 ( 4 + 95) \\= 10 \times 99 \\= 990$

Therefore.,

$\red{ Sum \:of \: 20 \: terms S_{20}} \green {= 990}$

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