Question

Ex. (1) Find the sum of first n natural numbers. Solution : First n natural numbers are 1, 2, 3, . . . , n. Here a = ……………………….., d = ……………., nth term =..........n

Answer 1

Question:

Find the sum of first n natural numbers. Solution : First n natural numbers are 1, 2, 3, . . . , n.

To find:

★ Sum of first n natural numbers.

★ a ( first term )

★ d ( common difference )

★ n th term

Answer:

$\bigstar \underline{ \: \underline{ \: \sf \pink{ \bold{a = 1}} \: } \: }$

$\bigstar \underline{ \: \underline{ \: \sf \red{ \bold{d = 1}} \: } \: }$

$\bigstar \underline{ \: \underline{ \: \sf \pink{ \bold{t _{n} = n}} \: } \: }$

$\bigstar Sum \: of \: first \: n \: natural \: numbers = \sf\red{\bold{\frac{n(n - 1)}{d}}}$

Step-by-step explanation:

$1, 2, 3, ... ....... . , n$

$First \: term \: \underline{(a) = 1}$

$Common \: difference \: \underline{(d) = t _{2} - t_{1}}$

$t _{1} = 1$

$t _{2} = 2$

$d = 2 - 1$

$\underline{ \: d = 1 \: }$

${n}^{th} \: term \boxed{ t _{n} = a + (n - 1)d}$

Now substituting the values,

$\implies 1 + (n - 1)1$

$\implies 1 + n - 1$

$\implies \boxed{t _{n} = n}$

$1, 2, 3, ... ....... . , n$

$Sum \: of \: first \: n \: natural \: numbers = \underline{\frac{n(n - 1)}{d}}$