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A sequence contains list of values in an ordered way. All these values are called as terms. Sum of first p terms in of a sequence is

Here i is the index of summation

1 is the lower limit and

P is the upper limit

1 is the lower limit and

P is the upper limit

There are different types of sequences or progressions.

- Arithmetic Progression
- Geometric Progression
- Harmonic Progression

A X H = G²

Here A stands for Arithmetic mean

H stands for Harmonic mean and

G stands for Geometric mean

Here A stands for Arithmetic mean

H stands for Harmonic mean and

G stands for Geometric mean

1) Fourth and tenth terms in a arithmetic sequence are 48 and 36 respectively. Find the general term of the sequence.

Answer:

General term of Arithmetic sequence is t_{n} = a + (n-1)d

For fourth term n= 4

t_{4} = a + (4-1)d

48 = a+3d

a = 48 – 3d

For tenth term n = 10

t_{10} = a + (10-1)d

36 = a + 9d

Substitute a = 48 – 3d in 36 = a+ 9d

36 = 48 – 3d + 9d

36 = 48 + 6d

6d = -12

d = -2

Substitute d = -2 in 48 = a+3d

48 = a + 3(-2)

48 = a -6

a = 54

General term t_n = 54 + (n-1)-2

t_{n} = 54 -2n +2

t_{n} = 56 – 2n