Question

Arithmetic
Progression

a= 1 ( first term )
d= 3. (common difference)
Sn= 287 ( sum)
find: n​

Answer 1

Answer:

number of term=14

Step-by-step explanation:

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Answer 2

Given:-

a$\implies$ 1

d$\implies$ 3

Sn$\implies$ 287

To Find:-

n$\implies$ ?

Solution:-

Sn = $\frac{n}{2}$[2a+(n-1)d] = 287

$\implies$ $\frac{n}{2}$[2×1+(n-1)3] = 287

$\implies$$\frac{n}{2}$(2+3n-1) = 287

$\implies$$\frac{n}{2}$(3n-1) = 287

$\implies$3n²-n = 287×2

$\implies$3n² - n - 574 = 0

$\implies$ 3n² - 42n + 41n - 574 = 0

$\implies$3n(n-14)+41(n-14) = 0

$\implies$(3n+41)(n-14) $\implies$0

Now taking 3n+41 = 0

we get,

n $\implies$ $\frac{-41}{3}$

Similarly, taking n-14 = 0

we get,

n $\implies$ 14