Question

7th term of an arithmetic sequence is 40:13th term is 76 a)find 19th term​

Answer 1

Step-by-step explanation:

t7 = 40, t13 = 76.

tn = a+(n-1)d

t7 = a+(7-1)d

a + 6d = 40. (I)

Also, t13 = a + (13-1)d

a + 12d = 76. (II)

Subtracting eq.(I) from eq. (II),

a + 12d = 76

-a + 6d = 40

(-) (-) (-)

6d = 36

d = 36/6 = 6

Substituting d=6 in (I),

a + 6(6) = 40

a + 36 = 40

a = 40-36

a = 4

tn = a+(n-1)d

Now, n = 19.

t19 = 4 + (19-1)6

= 4 + 18(6)

= 4 + 108

t19 = 112

The 19th term of the Arithmetic Sequence is 112.