Find the sum of first 20 terms the sequence whose nth term is an = A

1.	Find the sum of first 20 terms the sequence whose nth term is an = An + B.
Answer» Given an A.P. whose nth term is given by, a_n = An + 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, S_n = \(\frac{n(a \,+\, l)}{2}\) Where, a = the first term l = the last term, Putting n = 1 in the given 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 = \(\frac{20}{2}\)((A + B) + 20A + B) = 10[21A + 2B] = 210A + 20B Therefore, the sum of the first 20 terms of the given A.P. is 210 A + 20B

Find the sum of first 20 terms the sequence whose nth term is an = An + B.

Answer»

Given an A.P. whose nth term is given by, a_n = An + 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,

S_n = \(\frac{n(a \,+\, l)}{2}\)

Where, a = the first term l = the last term,

Putting n = 1 in the given 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 = \(\frac{20}{2}\)((A + B) + 20A + B)

= 10[21A + 2B]

= 210A + 20B

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