Question

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Answer 1

1. Find the sum of first twenty terms of A•P 2+7+12+........... using suitable formula

☯️Solution:-

• Formula used:- Sn = n/2[2a+(n-1)d]

In which n=no. of terms , a=first term , d= common difference and Sn=sum of nth term

We have the given Arithematic progression

2,7,12.......

Here a= 2, d= 5 and n= 20

Now we know the formula

$\red{\boxed{\mapsto\sf \: S_n = \dfrac{n}{2} \{a + (n - 1)d \}}\bigstar}$

Thus putting all the values

$\mapsto\sf \: S_{20} = \dfrac{20}{2} \{2 + (20 - 1)5\}$

$\mapsto\sf \: S_{20} = 10 \{2 + (19)5\}$

$\mapsto\sf \: S_{20} = 10\{2 + 19 \times 5\}$

$\mapsto\sf \: S_{20} = 10 \times 97$

$\blue{ \boxed{\mapsto\sf \: S_{20} = 970}}$

Thus , sum of first twenty terms of AP is 970.

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2.How many two digit number is divisible by 3.

☯️Solution:-

All two digit number which is divisible by 3 are

3, 6, 9,......99

This forms an ap where first term (a)= 3 and common difference (d)=3 and last term of AP (an) = 99

Now using formula

$\orange{ \boxed{ \mapsto\sf \: a _{n} = a + (n - 1)d}\bigstar}$

$\mapsto\sf \:99= 3 + (n- 1)3$

$\mapsto\sf \:99 = 3 +3n - 3$

$\sf \mapsto \: 3n \: = 99$

$\sf \mapsto \: n = \dfrac{99}{3}$

$\purple{ \boxed{\sf \mapsto \: n = 33}}$

Thus, total 33 , two digit numbers are divisible by 3.