Question
Download Solution PDFThe middle term of arithmatic series 2, 6, 10, ...,146
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Let us consider sequence a1, a2, a3 …. an is an A.P.
- Common difference “d”= a2 – a1 = a3 – a2 = …. = an – an – 1
- nth term of the A.P. is given by an = a + (n – 1) d
Calculation:
Given series is 2, 6, 10, ...,146
First term, a = 2, last term, an = 146, an
Common difference d = 4, so it is an AP
an = a + (n – 1) d
146 = 2 + (n - 1) (4)
⇒ n - 1 = 144/4
⇒ n = 36 + 1 = 37
So, number of terms in given series = 37
Middle term = (37 + 1)/2 = 19th term
a19 = 2 + (19 - 1) × 4
= 2 + 72
= 74
Hence, option (3) is correct.
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