Question

for an A.P the first term is 4 and the last term is (tn) is 31.the sum of all terms is 420 what is the value of n

Answer 1

$\mathtt{a = 4}$

$\mathtt{l = T_{n} = 31}$

$\mathtt{S_{n} = 420}$

$\mathtt{S_{n} = \frac{n}{2} (a+l)}$

$\mathtt{\implies 420 = \frac{n}{2} (4+31)}$

$\mathtt{\implies 420 = \frac{n}{2}×35}$

$\mathtt{\implies \frac{420×2}{35} = n}$

$\mathtt{\implies n = 24}$