Question

Find the middle term of AP 1,8,15........505​

Answer 1

Answer:

The given AP has:

first term a = 1

common difference d = (8 - 1) = (15 - 8) = 7

If 505 is the nth term then:

a + (n - 1)d = 505

=> 1 + (n - 1)*7 = 505

=> 7(n - 1) = 504

=> n - 1 = 72

=> n = 73

The middle term is (73 + 1)/2 = 37

Set n = 37 in the formula for nth term : a + (n - 1)d

Thus: 37th term

= a + (37 - 1)d

= 1 + 36*7

= 253

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Answer 2

Answer:

MIDLE TERM IS 37

AND A³⁷= 253

Step-by-step explanation:

first we'll find n= no. of terms,

An = a+(n-1) *d,

505=1+(n-1)*7,

505-1=(n-1)*7,

504=(n-1)*7,

504/7=(n-1),

72=n-1,

72+1=n,

73=n,

n=73.

now

the middle term =

= 73

= 72+1

=72/2+1

=36+1

= 37

An=a+(n-1)*d

A³⁷= 1 +(37-1)*7

A³⁷= 1 +(36)*7

A³⁷= 1 + 252

A³⁷=253

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