Question

The 12th term of an AP is 30 then the sum of its 5th, 12th and 19th term is—
Options: 90/30/60/45

Answer 1

Answer:

90

Step-by-step explanation:

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Given, 12th term of an Ap is 30

we know, n th term of Ap = a + (n - 1)d

where, a = first term, d = common difference, n = term

so, a12 = a + (12 - 1)d = 30

=> 30 = a + 11d ------------- ( 1 )

we have to find sum of 5th term, 12th term and 19th term

so, a5 + a12 + a19

=> {a + (5 - 1)d }+ {a + (12 - 1)d} + {a + (19 - 1)d}

=> a + 4d + a + 11d + a + 18d

=> 3a + 33d

=> 3(a + 11d)

from equation ---- ( 1 )

=> 3(30) = 90

therefore, sum of 5th , 12th and 19th term= 90

thank,

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Answer 2

The sum of its 5th, 12th and 19th term is 90.

Given data:

The 12th term of an A.P. is 30

To find:

The sum of its 5th, 12th and 19th term

Concept:

Let, a be the first term and d be the common difference of any given A.P.

Then the n-th term = a + (n - 1) d

Step-by-step explanation:

Let, a be the first term and d be the common difference of the given A.P.

Given, 12th term = 30

➜ a + (12 - 1) × d = 30

➜ a + 11d = 30 ... ... (1)

Now the sum of the 5th, 12th and 19th term of the A.P.

= {a + (5- 1) d} + {a + (12 - 1) d} + {a + (19 - 1) d}

= a + 4d + a + 11d + a + 18d

= 3a + 33d

= 3 (a + 11d)

= 3 × 30, by (1)

= 90

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