Question

if an AP an=3n+2 fir d the sun of first 20 term? ​

Answer 1

Answer:

${ \huge{ \underline{ \pmb{ \sf{ \red{Required \: Answer:}}}}}}$

In question they given that, an = 3n + 2

For Finding Sum of first 20 terms, we want a value and d value

Let's find a, d values:

$: \: \to{ \sf{ a_{n} = 3n + 2 }} \\ \\ : \: \to{ \sf{ a_{1} = 3(1)+ 2 }} \\ \\ : \: \to{ \sf{ a_{1} = 3 + 2 }} \\ \\ : \: \to{ \sf{ a_{1} = 5}}$

So, The first term in AP = 5

$\: : \: \to{ \sf{ a_{n} = 3n + 2 }} \\ \\ : \: \to{ \sf{ a_{2} = 3(2) + 2 }} \\ \\ : \: \to{ \sf{ a_{2} = 6 + 2 }} \\ \\ : \: \to{ \sf{ a_{2} = 8}}$

So, The second term = 8

Let's find common difference:

${ \sf{Common \: Difference = a_{2} - a}} \\ \\ { \sf{Common \: Difference = 8 - 5}} \\ \\ { \sf{Common \: Difference = 3}}$

So, The common difference = 3

Let's Find sum of 1st 20 terms:

$: { \implies{ \sf{ s_{n} = \frac{n}{2} (2a + (n - 1)d)}}} \\ \\ : { \implies{ \sf{ s_{20} = \frac{20}{2} \bigg[2(5) + (20 - 1)(3) \bigg]}}} \\ \\ : { \implies{ \sf{ s_{20} = 10\bigg[10 + 19(3)\bigg]}}} \\ \\ : { \implies{ \sf{ s_{20} = 10\bigg[10 + 57 \bigg]}}} \\ \\ : { \implies{ \sf{ s_{20} = 10(67 )}}} \\ \\ : { \implies{ \sf{ s_{20} =670}}}$

Therefore,

• Sum of first 20 terms = 670