Question

How many terms are there in an AP whose first term and sixth term are -12 and 8 respectively and sum of all its items is 120

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given,

First-term 'a' = -12

Sixth term a6 = 8

Sum  = 120

To find,

We have to find the number of terms in an AP.

Solution,

The number of terms in an AP whose first term and the sixth terms are -12 and 8 respectively and the sum of all its items is 120 is 12.

We can simply find the number of terms in an AP by using the formula of AP.

a = -12

a6 = a + (6-1)d

8  = -12 + 5d

20 = 5d

d   = 4

Sn = 120

Sn = n/2 (2a + (n-1)d)

120 = n/2 (-24 +(n-1)4)

120 = n/2 (-24 + 4n -4)

120 = n/2 (-28 +4n)

120 = n(-14 + 2n)

120 = -14n + 2n²

n² - 7n -60

n² -12n + 5n -60

n( n-12) +5 ( n-12)

(n-12) (n+5)

n = -5, 12

Hence, there are 12 terms in an AP whose first term and the sixth term are -12 and 8 respectively and the sum of all its items is 120.