Question

Find the 18th term from last term of the AP-3,-10,-17,...........,-276

Answer 1

Answer:

Last term = -276

difference = -7

18th Term = l - (n -1)d

18th Term = -276 - ( 18-1)(-7)

18th Term = -276 + 119

18th Term = - 157

The 18th term from the last term is -157.

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Answer 2

The 18th term from the last term = -150

An arithmetic progression (AP) is a set of terms in which the differences between each pair of words are the same.

The series 2, 6, 10, 14,..., for example, is an arithmetic progression (AP) because each number is obtained by adding 4 to the preceding term. nth term = 4n-2 in this sequence.

Formula for the $n^{th}$ term in an AP is given by

$a_{n}$ = $a_{0}$ + (n-1)d

where,

$a_{n}$ =  $n^{th}$ term in the AP

$a_{0}$ = first term of the AP

d = common difference.

In the given AP,

d = -7

Last term of the AP is -276.

∴ -276 = -3 + (n-1)-7

∴ n = 40

The 18th term from the last term = 40 - 18 = 22nd term

∴ n =22

Substituting in the formula,

$a_{22}$ = -3 + (22-1)× -7

∴ $a_{22}$ = -3 + 21 × -7

∴ $a_{22}$ = -3 - 147

∴ $a_{22}$ = -150