International Business Machines Corp. yesterday reported its third consecutive decline in quarterly earnings but held out hope to investors that it would enjoy significant growth in this last quarter of the year.

The world's largest computer company said its third-quarter earnings fell 7.7 percent from the same quarter a year ago in part due to softness in the economy as well as slower orders for its mainframe computers as customers awaited the introduction of IBM's new line of "Sierra" 3090 models.

IBM reported that earnings dropped from $1.58 billion from the third quarter of 1984 to $1.47 billion this past third quarter, representing a decline to $2.40 a share from $2.60 last year. The $2.40 per share was on the low end of many security analysts' estimates. Net earnings dropped even though gross income for the quarter climbed more than $1 billion from $10.66 billion to $11.7 billion compared with a year ago.

Analysts were split over the implications of this quarter's earnings report in the midst of the computer industry's and IBM's disappointing performance throughout this year.

"If you take the numbers apart, without the early delivery of the 3090s originally set for delivery in the fourth quarter of the year , total revenues were probably off," said Richard E. Imershein, vice president for research at the Gartner Group, a Connecticut-based computer industry research firm, which describes itself as "bearish" on IBM at this time.

IBM also stood to benefit from the recent decline in the dollar but company Chairman John Akers said the benefits of the lower dollar would be realized in the fourth quarter.

Moreover, Imershein and other analysts pointed out that IBM enjoyed a lower tax rate -- 42 percent verus 45 percent, according to some calculations -- that may have added up to 12 cents a share to earnings.

However, the engine of IBM's growth for the fourth quarter should be the sales of its 3090 computers, which analysts believe will enjoy tremendous success.

"Clearly, they're going to ship a lot of 3090s," said Imershein, "The question is, will they ship enough in the fourth quarter to give IBM an up year in terms of profits."

According to estimates, IBM would need at least a 24 percent jump in fourth-quarter earnings to attain profitability over 1984 levels.

IBM stock gained 1 1/4 to close at 125 3/8 yesterday, on volume of 1.38 million shares.