Question

if for A.P a=1, S20=1340, find d​

Answer 1

Answer:

• The common difference (d) is 6.95

Given:

• For an A.P., first term (a) = 1

• S20 = 1340

To find:

• Common difference (d).

Solution:

$\boxed{\sf{S_{n}=\dfrac{n}{2}[2a+(n-1)d]}} \\ \\ \sf{\therefore{S_{20}==\dfrac{20}{2}[2(1)+(20-1)d]}} \\ \\ \sf{\therefore{1340=10[2+19d]}} \\ \\ \sf{\therefore{2+19d=134}} \\ \\ \sf{\therefore{19d=132}} \\ \\ \sf{\therefore{d=\dfrac{132}{19}}} \\ \\ \sf{\therefore{d=6.95(approx)}} \\ \\ \purple{\tt{\therefore{The \ common \ difference \ is \ 6.95}}}$