Question

1) If the first term of AP is 1 and the nth term is 20.
If Sn = 399, then find n? .
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Answer 1

Answer:

a = 1

an = 20

Sn = 399

n = ?

Sn = n/2 ( a + an)

399 = n/2 ( 1 + 20)

399 × 2/ 21 = n

19 × 2 = n

n = 38

Answer 2

Given :-

The first term of an A.P. is 1 and the nth term is 20. If Sn = 399

To find :-

The value of n ?

Solution :-

The sum of n terms of A.P is given by,

$\sf\blue{S_n=\dfrac{n}{2}[a+l]}$

Where, a is the first term a=1

l is the nth term l=20

$\sf S_n=399$is the sum of n terms

Substitute the value in the formula,

$\sf 399=\dfrac{n}{2}[1+20]\\ \sf798=21n\\ \sf n=\dfrac{798}{21}\\ \sf n=38$

$\sf{\boxed {\therefore The\: value\: of\: n\: is\: 38.}}$