Question

in an AP given a=5,d=3,,an=50,findn and sn

Answer 1

Hey there!

Given,

$a = 5$

$d = 3$

$a {n} = 50$

$n = (\frac{an - a}{d} ) + 1$

$n = ( \frac{50 - 5}{3} )$

$n = \frac{45}{3}$

$n = 15$

$sn = \frac{n}{2} ( 2a + (n - 1)d)$

$\frac{15}{2} (2 \times 5 + (15 - 1)3)$

$\frac{15}{2} \times 10 + 14 \times 3$

= 390.

So, n = 15
sn = 390

Glad if helped.

Answer 2

Answer:

Given -

• a = 5
• d = 3
• $\sf{a}_{n}$ = 50

We know that ,

$\\ \sf \: a_n = a + (n - 1) \: d \\ \\ \\ \implies \sf \: 50 = 5 + (n - 1) \: 3 \\ \\ \\ \implies \sf \: 50 - 5 = (n - 1) \: 3 \\ \\ \\ \implies \sf \: n - 1 = \cancel \dfrac{45}{3} \\ \\ \\ \implies \sf \: n - 1 = 15 \\ \\ \\ \implies \sf \: n = 1 + 15 \\ \\ \\ \implies \large{ \underline{ \boxed {\sf{ \blue{n = 16}}}}}$

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$\\ \\ \sf \: s_n = \dfrac{n}{2} \bigg( \: 2a + (n - 1) \: d \bigg) \\ \\ \\ \implies \sf \: \dfrac{n}{2} \: \bigg( \: a + \underline{ a + (n - 1) \: d} \bigg) \\ \\ \\ \implies \sf \: \dfrac{n}{2} \: \bigg( \: a + a_n \bigg) \\ \\ \\ \implies \sf \: s_{16} = \cancel\dfrac{18}{2} \: \bigg(5 + 50 \bigg) \\ \\ \\ \implies \sf \: s_{16} = 8 \times 55 \\ \\ \\ \implies \large{ \underline{ \boxed {\sf{ \green{s_{16} = 440}}}}}$