Question

the first term and the common different of an ap is 10 and 5 respectively the fund the sum of first 30 terms​

Answer 1

Step-by-step explanation:

Sn= n/2  [2a+(n-1)d]

S30=30/2  [20+(30-1)*5

= 15[20+145]

=15*165

=2475

Answer 2

AnswEr

• First term $\sf a_{1} = 10$
• Common Difference (d) = 5

We've to find sum of the first 30 terms.

To find the sum of an AP Formula is given as :

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀ ⠀⠀⠀

$\star\ \boxed{\sf{\purple{S_{n} = \dfrac{n}{2}\Bigg(2a + [n - 1] d \Bigg)}}}$

Substituting values :

$:\implies\sf S_{30} = \dfrac{\cancel{30}}{\cancel{\:2}}\Bigg( 2(10) + [30 - 1] 5 \Bigg) \\\\\\:\implies\sf S_{30} = 15 \Bigg(20 + 29 \times 5 \Bigg) \\\\\\:\implies\sf S_{30} = 15\Bigg(20 + 145 \Bigg)\\\\\\:\implies\sf S_{30} = 15 \times 165\\\\\\:\implies\boxed{\frak{\pink{ S_{30} = 2475}}}$

Hence, Sum of first 30 terms is 2475.

⠀⠀⠀$\boxed{\bf{\mid{\overline{\underline{\bigstar\: Formulaes \ : }}}}\mid}$⠀⠀

$\begin{lgathered}\boxed{\begin{minipage}{15 em} \sf \displaystyle \bullet a_n=a + (n-1)d \\\\\\ \bullet S_n= \dfrac{n}{2} \left(a + a_n\right) \end{minipage}}\end{lgathered}$