Question

If the first term is equals to the common difference and the 2nd term is 10, then find the sum of first 20 terms.
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Answer 1

given, a=d

given, 2nd term= 10

2nd term = a+d

10 = a+d

10 = 2a

a = 10/2

a=d= 5

tap the above attachment for the rest of the answer

final answer is 1050

Answer 2

Given,

The first term is equal to the common difference.

T₂ = 10

To find,

The sum of the first 20 terms

Solution,

The sum of the first 20 terms is 1050.

We can simply solve the mathematical problem by the following process.

We know that,

a = d  (Equation 1)

T₂ = 10  (Equation 2)

Now,

∴ T₂ = 10

⇒ a + d = 10

⇒ 2a = 10 ( From equation 1)

⇒ a = 5

Thus,

⇒ a = d = 5

As we know,

Sₙ = $\frac{n}{2} (2a + (n-1)d)$

Thus,

S₂₀ = $\frac{20}{2} (2*5 + (20 - 1)5)$

     = 10 (10 + 19 * 5)

     = 10 ( 10 + 95)

     = 10 * 105

     = 1050

As a result, the sum of the first 20 terms is 1050.