Question

fifth term of an A.P. is 13 and sum of its first 15 term is 285. find 14th term of this A.P. and also first n term

Answer 1

heya!!!

Nth term of A.P is = a + ( n - 1 ) d

where a is ist term and d is common difference.

5th term = a + ( 5 - 1 ) d = 13

5th term = a + 4d = 13

Sum of ist 15 terms = 15 / 2 ( 2a + 14d ) = 285

15 / 2 ( 2 ( 13 - 4d ) + 14d ) = 285

d = 2 and a = 5

14th term = a + 13d

14th term = 5 + 13 ( 2 ) = 31

Have a nice time

Answer 2

Answer AND Step-by-step explanation:

• The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount.
• It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1).

• The nth term of A.P is = a + ( n - 1 ) d

where a is the first term and d is a common difference.

• 5th term = a + ( 5 - 1 ) d = 13

• 5th term = a + 4d = 13

• Sum of ist 15 terms = 15 / 2 ( 2a + 14d ) = 285

• 15 / 2 ( 2 ( 13 - 4d ) + 14d ) = 285

• d = 2 and a = 5

• 14th term = a + 13d

• 14th term = 5 + 13 ( 2 ) = 31

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