Question

Write the formula given the following arithmetic sequences.
tn = 1/2, 1 3/4, 3, 4 1/4, ...


tn = 5/4 + 1/2(n – 1)

tn = 1/2 – 5/4(n – 1)

tn = 1/2 + 5/4(n – 1)

tn = 1/2 + 3(n – 5/4)

Answer 1

See, General Formula for AP is given As:

\[t_n = a + (n - 1).d\]

Here, tn = Last term of AP,
n = Number of terms in AP
a = First term of AP,
d = Common Difference of AP..

Answer 2

common difference = 1 3/4 - 1/2 = 5/4

Answer 3

tn = a+ (n-1)d
so 1/2+5/4(n-1)

Answer 4

the series can be rewritten as 2/4, 7/4, 12/4, 17/4... so d= 5/4.. a= first term=1/2

Answer 5

So, the terms given are:

1/2, 7/4, 17/4, .....

d= 7/4 - 1/2 = 5/4

Or you can further check it: 3 - 7/4 = 5/4

So, the d = 5/4

and a = 1/2

Put these values in the formula written above and solve for tn...

Answer 6

Here I missed 3 in the terms given are...