Question

which term of AP 3,7,11,15.......is 79? also find the sum of 3+7+11+......+79

Answer 1

$tn = a + (n - 1) \times d \\ 79 = 3 + (n - 1) \times 4 \\ 79 = 3 + 4n - 4 \\ 79 = - 1 + 4n \\ 4n = 79 + 1 \\ 4n = 80 \\ n = \frac{80}{4} \\ n = 20 \\ sn = \frac{n}{2} (2a + (n - 1) \times d \\ s20 = \frac{20}{2} (2 \times 3 + (20 - 1) \times 4) \\ \: \: \: \: \: \: \: \: = 10(6 + 19 \times 4) \\ \: \: \: \: \: \: \: \: = 10 (6 + 76) \\ \: \: \: \: \: \: \: \: = 10 \times 82 \\ \: \: \: \: \: \: \: \: = 820$