What is the average of the first sixty terms of an arithmetic progression having the first term of progression is 20 and the difference in terms T18 and T7 is 44?

What is the average of the first sixty terms of an arithmetic progression having the first term of progression is 20 and the difference in terms T18 and T7 is 44? Correct Answer 138

Given,

⇒ Average = sum of terms/number of terms

For arithmetic progression,

If sum of terms = S_n and the first term of progression = a, common difference = d and n = number of terms, then –

S_n = (n/2)

T_n = a + (n – 1) d

Given,

⇒ T₁₈ = a + 17d

⇒ T₇ = a + 6d

⇒ 44 = a + 17d – a – 6d

⇒ 44 = 11d

⇒ d = 4

Given,

a = 20 and d = 4 and n = 60

⇒ S₆₀ = (60/2)

⇒ S₆₀ = 8280