Question

find the number of terms in an AP whose first term and 6th term are 12 and 8 respectively and sum of all terms is 120​

Answer 1

Sum of 120 terms is 120.

Step-by-step explanation:

★ Given that,

◼ First term of AP : -12

• a = -12

◼ 6th term of AP: 8

• a6 = 8

★ To find,

• Sum of 120 terms.

★ Let,

➠ a6 : a + 5d = 8

• Substitute value of a.

➠ -12 + 5d = 8

➠ 5d = 8 + 12

➠ 5d = 20

➠ d = 5

★ Now,

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

• n = 120
• a = - 12
• d = 5

➠ S120 = 120/2[ 2(-12) + (120 - 1)(5) ]

➠ S120 = 60[ -24 + 119(5) ]

➠ S120 = 60[ - 24 + 476 ]

➠ S120 = 60[452]

➠ S120 = 27120

∴ Hence, sum of 120 terms is “ 27120 ”.

★ More info :

Formula related to Arithmetic Progression :

☯ an = a + (n - 1)d

☯ Sn = n/2[ 2a + (n - 1)d ]

Where,

a = first term of AP.

n = number of terms of AP.

d = common difference(d) of AP.

an = nth term of AP.

Sn = sum of nth terms of AP.

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