Question

please answer my question​

Answer 1

Given,

An A.P. whose nth term is given by, $\sf{a_n~=~A_n~+~b}$

→ We need to find the sum of first 20 terms.

To find the sum of the n terms of the given A.P.,

we use the formula,

$\longrightarrow~\sf{S_n~=~\dfrac{n~(a~+~l)}{2}}$

Where,

• a = the first term

• l = the last term

Putting “n = 1” in the given $\sf{a_n}$ we get,

→ a = A(1) + B = A + B

For the last term (l), here n = 20

→ A₂₀ = A(20) + B = 20A + B

→ S₂₀ = $\sf{\dfrac{20}{2}~\bigg((A~+~B)~+~20A~+~B\bigg)}$

→ S₂₀ = 10 [21A + 2B]

→ S₂₀ = 210 A + 20B

Therefore, the sum of the first 20 terms of the given A.P. is (210 A + 20B).